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Vector Algebra question

2024 · Shift 1 · Q29

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2024 · Shift 1 · Q29

Vector Algebra question

2024 · Shift 1 · Q29

JEE AdvancedMathematicsVector AlgebraNumerical+4 / −1

Let

\overrightarrow{O P}=\frac{\alpha-1}{\alpha} \hat{i}+\hat{j}+\hat{k}, \overrightarrow{O Q}=\hat{i}+\frac{\beta-1}{\beta} \hat{j}+\hat{k}

and

\overrightarrow{O R}=\hat{i}+\hat{j}+\frac{1}{2} \hat{k}

be three vectors, where

\alpha, \beta \in \mathbb{R}-\{0\}

and

O

denotes the origin. If

(\overrightarrow{O P} \times \overrightarrow{O Q}) \cdot \overrightarrow{O R}=0

and the point

(\alpha, \beta, 2)

lies on the plane

3 x+3 y-z+l=0

, then the value of

l

is

\underline{\hspace{2cm}}

.

Numerical answer

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