JEE Main 2024 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 4 April 2024, Shift 2, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

For

\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

. If the vectors

\vec a+\vec b

and

\vec a-\vec b

are mutually perpendicular, then the value of

(14\cos\theta)^2

is equal to

(1)25Official answer
(2)20
(3)50
(4)40

Official answer

Option 1

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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25 Jul 2021, Shift 2 · Q88If $\left(\vec{a}+3\vec{b}\right)$ is perpendicular to $\left(7\vec{a}-5\vec{b}\right)$ and $\left(\vec{a}-4\vec{b}\right)$ is…MediumNumerical value
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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.