28:["$","li","0",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":1}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"Equation of plane passing through (2, 1, 2)"}}]]}] 37:T59f,a(x

-

2) + b(y

-

1) + c(z

-

2) = 0 ......(1)29:["$","li","1",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":2}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$37"}}]]}] 2a:["$","li","2",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":3}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"As point (1, 2, 1) also passes through the plane, so it satisfy the equation,"}}]]}] 38:T595,a(1

-

2) + b(2

-

1) + c(1

-

2) = 02b:["$","li","3",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":4}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$38"}}]]}] 39:T57c,

\Rightarrow

-

a + b

-

c = 0 ....(2)2c:["$","li","4",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":5}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$39"}}]]}] 2d:["$","li","5",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":6}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"Given line 2x = 3y and z = 1,"}}]]}] 2e:["$","li","6",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":7}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"So, symmetric form of the line"}}]]}] 3a:Tf37,

{x \over 3} = {y \over 2} = {{z - 1} \over 0}

2f:["$","li","7",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":8}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$3a"}}]]}] 30:["$","li","8",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":9}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"

\\therefore

Direction ratio of this line is (3, 2, 0) and Direction ration of plane = (a, b, c)"}}]]}] 31:["$","li","9",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":10}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"As plane is parallel to the line so the normal of the plane is perpendicular to the line."}}]]}] 32:["$","li","10",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":11}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"

\\therefore

Dot product of direction ratio = 0"}}]]}] 33:["$","li","11",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":12}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"3a + 2b + 0(c) = 0 .....(3)"}}]]}] 34:["$","footer",null,{"className":"flex flex-wrap gap-2 border-t border-rule pt-4 text-[13px] text-ink-400","children":["JEE Main 2020 · 2 Sep, Morning shift · Q2424",["$","span",null,{"className":"text-rule-strong","children":"·"}],"3d Geometry"]}] 35:["$","section",null,{"className":"flex flex-col gap-3 border-t border-rule pt-6","children":[["$","h2",null,{"className":"m-0 text-[12px] font-semibold uppercase tracking-[0.06em] text-ink-400","children":["More on ","3d Geometry"]}],["$","ul",null,{"className":"m-0 flex list-none flex-col gap-2 p-0","children":[["$","li","9fe5045c-9959-41ec-bda2-8f2822bf21c7",{"children":["$","$L8",null,{"href":"/q/the-distance-between-the-line-overrightarr-LrYeTFfhmmgV6ZGq","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"3d Geometry"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2005 · Annual, Paper 1 · Q2389"}]]}]}],["$","li","8f1bcc26-aef4-4f3c-a098-46ecd57bdb40",{"children":["$","$L8",null,{"href":"/q/if-the-plane-passes-through-nTl94Fj4X6KBIr3k","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"3d Geometry"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2005 · Annual, Paper 1 · Q2388"}]]}]}],["$","li","3aa3b696-ea43-43c3-ab52-2060d4317481",{"children":["$","$L8",null,{"href":"/q/the-two-lines-and-x-a-y-kt4Qsk8Vq7TCfuAU","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"3d Geometry"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2003 · Annual, Paper 1 · Q2368"}]]}]}],["$","li","93bf1103-51d9-4161-8666-e8b1779ef820",{"children":["$","$L8",null,{"href":"/q/a-line-makes-the-same-angle-with-ea-UTyglZ3FzG2VUgaZ","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"3d Geometry"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2004 · Annual, Paper 1 · Q2369"}]]}]}]]}]]}]

More on 3d Geometry

More on 3d Geometry