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Vector Algebra question

2021 · Shift 2 · Q24

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2021 · Shift 2 · Q24

Vector Algebra question

2021 · Shift 2 · Q24

JEE AdvancedMathematicsVector AlgebraMultiple correct+4 / −2

Let O be the origin and

\overrightarrow {OA} = 2\widehat i + 2\widehat j + \widehat k

and

\overrightarrow {OB} = \widehat i - 2\widehat j + 2\widehat k

and

\overrightarrow {OC} = {1 \over 2}\left( {\overrightarrow {OB} - \lambda \overrightarrow {OA} } \right)

for some

\lambda

> 0. If

\left| {\overrightarrow {OB} \times \overrightarrow {OC} } \right| = {9 \over 2}

, then which of the following statements is (are) TRUE?

A
Projection of $\overrightarrow {OC}$ on $\overrightarrow {OA}$ is $- {3 \over 2}$
B
Area of the triangle OAB is ${9 \over 2}$
C
Area of the triangle ABC is ${9 \over 2}$
D
The acute angle between the diagonals of the parallelogram with adjacent sides ${\overrightarrow {OA} }$ and ${\overrightarrow {OC} }$ is ${\pi \over 3}$

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