Let $OABC$ be a parallelogram, $O$ be the origin, $A\,(2, 4, -5)$ and $C\,(b, 2, 3)$. If $P\,(a, a, a)$ and $Q\,(9-a^2, 3, a-1)$, $a \in \mathbb{N}$, are two points such that the projection of $\overrightarrow{OP}$ on $\overrightarrow{OB}$ is 2 and $\overrightarrow{OQ}$ makes acute angles with all three co-ordinate axes, then $\left|\overrightarrow{OB}\right|^2 + \left|\overrightarrow{AC}\right|^2$ is equal to ________.

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q88

Question 88 of 90 in this shift, Maths question 28 of 30, Section B.

Let

OABC

be a parallelogram,

O

be the origin,

A\,(2, 4, -5)

and

C\,(b, 2, 3)

. If

P\,(a, a, a)

and

Q\,(9-a^2, 3, a-1)

a \in \mathbb{N}

, are two points such that the projection of

\overrightarrow{OP}

\overrightarrow{OB}

is 2 and

\overrightarrow{OQ}

makes acute angles with all three co-ordinate axes, then

\left|\overrightarrow{OB}\right|^2 + \left|\overrightarrow{AC}\right|^2

is equal to ________.

Official answer

118

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Scalar and Vector Projection

Same idea in other shifts

Asked 11× in all

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26 Jun 2022, Shift 2 · Q16Let $\vec{a} = \hat{i} + \hat{j} + 2\hat{k}$ , $\vec{b} = 2\hat{i} - 3\hat{j} + \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + \hat{k}$ be…MediumSingle correct
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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.