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Vector Algebra question

2025 · Shift 2 · Q28

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2025 · Shift 2 · Q28

Vector Algebra question

2025 · Shift 2 · Q28

JEE AdvancedMathematicsVector AlgebraNumerical+4 / −1

Consider the vectors

\vec{x}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k}, \quad \vec{y}=2 \hat{\imath}+3 \hat{\jmath}+\hat{k}, \quad \text { and } \quad \vec{z}=3 \hat{\imath}+\hat{\jmath}+2 \hat{k}

For two distinct positive real numbers

\alpha

and

\beta

, define

\vec{X}=\alpha \vec{x}+\beta \vec{y}-\vec{z}, \quad \vec{Y}=\alpha \vec{y}+\beta \vec{z}-\vec{x}, \quad \text { and } \quad \vec{Z}=\alpha \vec{z}+\beta \vec{x}-\vec{y} .

If the vectors

\vec{X}, \vec{Y}

, and

\vec{Z}

lie in a plane, then the value of

\alpha+\beta-3

is

\underline{\hspace{2cm}}

.

Numerical answer

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