JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q15

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

Let

\vec{a}

and

\vec{b}

be the vectors along the diagonals of a parallelogram having area

2\sqrt{2}

. Let the angle between

\vec{a}

and

\vec{b}

be acute,

|\vec{a}|=1

, and

|\vec{a}\cdot\vec{b}|=|\vec{a}\times\vec{b}|

. If

\vec{c}=2\sqrt{2}\left(\vec{a}\times\vec{b}\right)-2\vec{b}

, then an angle between

\vec{b}

and

\vec{c}

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

Official answer

Option 4

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Area of Quadrilateral via Diagonals

Same idea in other shifts

Asked 7× in all

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30 Jan 2024, Shift 1 · Q17Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $ABCD$ . If the diagonal…MediumSingle correct
8 Apr 2023, Shift 2 · Q15The area of the quadrilateral $ABCD$ with vertices $A(2, 1, 1)$ , $B(1, 2, 5)$ , $C(-2, -3, 5)$ and $D(1, -6, -7)$ is equal toMediumSingle 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.