Let O be the origin and \overline{O A}=2 \hat{i}+2 \hat{j}+\hat{k}, \overline{O B}=\hat{i}-2 \hat{j}+2 \hat{k} and \overrightarrow{O C}=\frac{1}{2}(\overrightarrow{O B}-\lambda \overrightarrow{O A}) for some \lambda>0. If |\overrightarrow{O B} \times \overrightarrow{O C}|=\frac{9}{2}, then which of the following statements is (are) TRUE? [JEE Adv 2021 P2]

Projection of \overrightarrow{O C} on \overline{O A} is -\frac{3}{2}

Area of the triangle O A B is \frac{9}{2}

Area of the triangle A B C is \frac{9}{2}

The acute angle between the diagonals of the parallelogram with adjacent sides \overline{O A} and \overline{O C} is \frac{\pi}{3}

Vector Algebra

Section: Mathematics

Question : 10 of 38

Marks: +1, -0

Let O be the origin and OA=2

∧

,OB=

∧

−2

∧

and

→

=‌

(

→

−λ

→

) for some λ>0. If |

→

|=‌

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

[JEE Adv 2021 P2]

Projection of
→
OC
on OA is −‌
3
2
Area of the triangle OAB is ‌
9
2
Area of the triangle ABC is ‌
9
2
The acute angle between the diagonals of the parallelogram with adjacent sides OA and OC is ‌
π
3

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