Let a=i+4 j+2 k, b=3 i-2 j+7 k and c=2 i-j+4 k. If a vector d satisfies d × b=c × b and d · a=24, then |d|² is equal to:

Vector Algebra: JEE Main 2023 Mathematics question

JEE Main 2023 · 13 Apr, Morning shift · Q5838

JEE Main 202313 Apr, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let

\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}

and

\vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}

. If a vector

\vec{d}

satisfies

\vec{d} \times \vec{b}=\vec{c} \times \vec{b}

and

\vec{d} \cdot \vec{a}=24

, then

|\vec{d}|^{2}

is equal to :

JEE Main 2023 · 13 Apr, Morning shift · Q5838

JEE Main 202313 Apr, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let

\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}

and

\vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}

. If a vector

\vec{d}

satisfies

\vec{d} \times \vec{b}=\vec{c} \times \vec{b}

and

\vec{d} \cdot \vec{a}=24

, then

|\vec{d}|^{2}

is equal to :