JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 2, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

A vector

\vec{a}

is parallel to the line of intersection of the plane determined by the vectors

\hat{i},\ \hat{i}+\hat{j}

and the plane determined by the vectors

\hat{i}-\hat{j},\ \hat{i}+\hat{k}

. The obtuse angle between

\vec{a}

and the vector

\vec{b}=\hat{i}-2\hat{j}+2\hat{k}

(1) $\frac{3\pi}{4}$ Official answer
(2) $\frac{2\pi}{3}$
(3) $\frac{4\pi}{5}$
(4) $\frac{5\pi}{6}$

Official answer

Option 1

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Direction of Line of Intersection

Same idea in other shifts

Asked 4× in all

27 Jul 2022, Shift 2 · Q15If the line of intersection of the planes $ax + by = 3$ and $ax + by + cz = 0$ , a > 0 makes an angle $30^\circ$ with the plane…MediumSingle correct
28 Jun 2022, Shift 1 · Q15If two distinct points Q, R lie on the line of intersection of the planes $-x+2y-z=0$ and $3x-5y+2z=0$ and $PQ=PR=\sqrt{18}$ where the…HardSingle correct
29 Jun 2022, Shift 1 · Q29Let $P_1: \vec{r}\cdot(2\hat{i} + \hat{j} - 3\hat{k}) = 4$ be a plane. Let $P_2$ be another plane which passes through the points…MediumNumerical value

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.