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 overrightarrow A ×(overrightarrow B × overrightarrow C )=0 , them value of x is .

Physics · Vectors and Scalars

JEE Main 2024 — 6 April, Shift 1 — Question 59

For three vectors $\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})$ , $\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k}) \quad$ and $\quad \vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k}), \quad$

if $\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0$ , them value of x is $\qquad$ .

Answer: 4

Numerical answer — enter this value.

Step-by-step solution

$\text{ }\!\!~\!\!\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{C}}=\left| \begin{matrix}\overset{\text{}}{\mathop{\text{i}}}\,&\overset{\text{}}{\mathop{\text{j}}}\, & \overset{}{\mathop{k}}\, \\-1 & 4 &3 \\-8 & -1 & 3 \\\end{matrix} \right|=15\overset{\text{}}{\mathop{\text{i}}}\,-21\overset{\text{}}{\mathop{\text{j}}}\,+33\overset{\text{}}{\mathop{\text{k}}}\,$

$\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=(-x \hat{i}-6 \hat{j}-2 \hat{k}) \cdot(15 \hat{i}-21 \hat{j}+33 \hat{k})$

$0=-15 x+126-66$

$15 \mathrm{x}=60$

$\mathrm{x}=4$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 6 April, Shift 1
Subject: Physics
Chapter: Vectors and Scalars
Topic: Product of Vectors and Applications