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JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q28

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

Let

\vec{a}=9\hat{i}-13\hat{j}+25\hat{k}

,

\vec{b}=3\hat{i}+7\hat{j}-13\hat{k}

and

\vec{c}=17\hat{i}-2\hat{j}+\hat{k}

be three given vectors. If

\vec{r}

is a vector such that

\vec{r}\times\vec{a}=(\vec{b}+\vec{c})\times\vec{a}

and

\vec{r}\cdot(\vec{b}-\vec{c})=0

, then

\frac{|593\vec{r}+67\vec{a}|^2}{(593)^2}

is equal to ____________.

Official answer

569

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Simultaneous Cross and Dot Equations

Same idea in other shifts

Asked 3× in all

2 Apr 2025, Shift 2 · Q16Let $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ , $\vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k}$ and a vector $\vec{c}$ be such that…MediumSingle correct
3 Apr 2025, Shift 2 · Q24Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}, \vec{b} = 3\hat{i} - 3\hat{j} + 3\hat{k}, \vec{c} = 2\hat{i} - \hat{j} + 2\hat{k}$ and…MediumNumerical value

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 42 of the 174 JEE Main shifts held from 2017 to 2026.