For three vectors A =(-x i -6 j -2 k ), B =(- i +4 j +3 k ) and C =(-8 i - j +3 k ) , if A ·( B × C )=0 , then value of x is _________

Correct answer: 0 aligned & B × C =| array ccc i & j & k -1 & 4 & 3 -8 & -1 & 3 array |=15 i -21 j +33 k & A ·( B × C )=(-x i -6 j -2 k ) ·(15 i -21 j +33 k ) & 0=-15 x+126-66 & 15 x=60 & x=4 aligned

JEE Main 20246 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Morning Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2024 · 6 April · Morning Shift · Physics · Mathematics in Physics

For three vectors A =(-x i -6 j -2 k ), B =(- i +4 j +3 k ) and C...

For three vectors

\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})

and

\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})

, if

\vec{A} \cdot(\vec{B} \times \vec{C})=0

, then value of

x

is _________

Correct answer

Step-by-step solution

\begin{aligned} & \vec{B} \times \vec{C}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ -1 & 4 & 3 \\ -8 & -1 & 3\end{array}\right|=15 \hat{i}-21 \hat{j}+33 \hat{k} \\ & \vec{A} \cdot(\vec{B} \times \vec{C})=(-x \hat{i}-6 \hat{j}-2 \hat{k}) \cdot(15 \hat{i}-21 \hat{j}+33 \hat{k}) \\ & 0=-15 x+126-66 \\ & 15 x=60 \\ & x=4\end{aligned}

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