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JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 8 April 2023, Shift 1, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

If the points with position vectors

\alpha\hat{i}+10\hat{j}+13\hat{k}

,

6\hat{i}+11\hat{j}+11\hat{k}

,

\frac{9}{2}\hat{i}+\beta\hat{j}-8\hat{k}

are collinear, then

(19\alpha-6\beta)^2

is equal to

(1) $16$
(2) $25$
(3) $36$ Official answer
(4) $49$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Linear Independence
Idea tested: Collinearity of Three Position Vectors

Same idea in other shifts

Asked 2× in all

29 Jun 2022, Shift 2 · Q15Let $A, B, C$ be three points whose position vectors respectively are $\vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}$ …EasySingle 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.