JEE Main 2021 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 26 February 2021, Shift 2, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

If vectors

\vec{a}_1 = x\hat{i} - \hat{j} + \hat{k}

and

\vec{a}_2 = \hat{i} + y\hat{j} + z\hat{k}

are collinear, then a possible unit vector parallel to the vector

x\hat{i} + y\hat{j} + z\hat{k}

is :

(1) $\frac{1}{\sqrt{2}}\left(-\hat{j}+\hat{k}\right)$
(2) $\frac{1}{\sqrt{3}}\left(\hat{i}-\hat{j}+\hat{k}\right)$ Official answer
(3) $\frac{1}{\sqrt{3}}\left(\hat{i}+\hat{j}-\hat{k}\right)$
(4) $\frac{1}{\sqrt{2}}\left(\hat{i}-\hat{j}\right)$

Official answer

Option 2

NTA final key.

Chapter: Vector Algebra
Topic: Linear Independence
Idea tested: Proportionality Test for Collinearity

Same topic in other shifts

All Linear Independence questions

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.