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Vector Algebra question

2024 · Shift 2 · Q28

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2024 · Shift 2 · Q28

Vector Algebra question

2024 · Shift 2 · Q28

JEE AdvancedMathematicsVector AlgebraNumerical+4 / −1

Let

\vec{p}=2 \hat{i}+\hat{j}+3 \hat{k}

and

\vec{q}=\hat{i}-\hat{j}+\hat{k}

. If for some real numbers

\alpha, \beta

, and

\gamma

, we have

15 \hat{i}+10 \hat{j}+6 \hat{k}=\alpha(2 \vec{p}+\vec{q})+\beta(\vec{p}-2 \vec{q})+\gamma(\vec{p} \times \vec{q}),

then the value of

\gamma

is

\underline{\hspace{2cm}}

.

Numerical answer

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