JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 July 2021, Shift 2, Maths Q88

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

\left(\vec{a}+3\vec{b}\right)

is perpendicular to

\left(7\vec{a}-5\vec{b}\right)

and

\left(\vec{a}-4\vec{b}\right)

is perpendicular to

\left(7\vec{a}-2\vec{b}\right)

, then the angle between

\vec{a}

and

\vec{b}

(in degrees) is __________.

Official answer

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Angle Between Vectors

Same idea in other shifts

Asked 6× in all

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4 Apr 2024, Shift 1 · Q18Let a unit vector which makes an angle of $60^\circ$ with $2\hat{i}+2\hat{j}-\hat{k}$ and an angle of $45^\circ$ with $\hat{i}-\hat{k}$ be…HardSingle correct
4 Apr 2024, Shift 2 · Q17Let $\vec a=\hat i+\hat j+\hat k,\ \vec b=2\hat i+4\hat j-5\hat k$ and $\vec c=x\hat i+2\hat j+3\hat k,\ x\in\mathbb{R}$ . If $\vec d$ is…MediumSingle correct
4 Apr 2024, Shift 2 · Q18For $\lambda>0$ , let $\theta$ be the angle between the vectors $\vec a=\hat i+\lambda\hat j-3\hat k$ and $\vec b=3\hat i-\hat j+2\hat k$ .…EasySingle correct
3 Sep 2020, Shift 2 · Q69Let a, b, $c \in \mathbf{R}$ be such that $a^2 + b^2 + c^2 = 1$ . If…HardSingle correct

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.