JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 September 2020, Shift 2, Maths Q69

Question 69 of 75 in this shift, Maths question 19 of 25.

Let a, b,

c \in \mathbf{R}

be such that

a^2 + b^2 + c^2 = 1

. If

a\cos\theta = b\cos\left(\theta + \frac{2\pi}{3}\right) = c\cos\left(\theta + \frac{4\pi}{3}\right)

, where

\theta = \frac{\pi}{9}

, then the angle between the vectors

a\hat{i} + b\hat{j} + c\hat{k}

and

b\hat{i} + c\hat{j} + a\hat{k}

is :

(1) $\frac{2\pi}{3}$
(2)0
(3) $\frac{\pi}{2}$ Official answer
(4) $\frac{\pi}{9}$

Official answer

Option 3

NTA final key (Sep 2020).

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

Same idea in other shifts

Asked 6× in all

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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.