JEE Main 2020 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 4 September 2020, Shift 2, Maths Q75

Question 75 of 75 in this shift, Maths question 25 of 25.

\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}

, then the value of

\left|\hat{i} \times (\vec{a} \times \hat{i})\right|^2 + \left|\hat{j} \times (\vec{a} \times \hat{j})\right|^2 + \left|\hat{k} \times (\vec{a} \times \hat{k})\right|^2

is equal to ________.

Official answer

18.00

NTA final key (Sep 2020).

Chapter: Vector Algebra
Topic: Triple Products
Idea tested: Perpendicular Vector Component via VTP

Same topic in other shifts

All Triple Products questions

6 Apr 2024, Shift 2 · Q18Let $\vec{a}=2\hat{i}+\hat{j}-\hat{k}$ , $\vec{b}=\left(\left(\vec{a}\times(\hat{i}+\hat{j})\right)\times\hat{i}\right)\times\hat{i}$ . Then…MediumSingle correct
1 Feb 2024, Shift 1 · Q19Let $\vec{a}=-5\hat{i}+\hat{j}-3\hat{k}$ , $\vec{b}=\hat{i}+2\hat{j}-4\hat{k}$ and…MediumSingle correct
6 Apr 2023, Shift 1 · Q15Let the position vectors of the points A, B, C and D be $5\hat i+5\hat j+2\lambda\hat k$ , $\hat i+2\hat j+3\hat k$ ,…MediumSingle correct
6 Apr 2023, Shift 2 · Q17The sum of all values of $\alpha$ , for which the points whose position vectors are $\hat{i}-2\hat{j}+3\hat{k}$ ,…MediumSingle correct
6 Apr 2023, Shift 2 · Q18Let the vectors $\vec{a},\vec{b},\vec{c}$ represent three coterminous edges of a parallelopiped of volume V. Then the volume of the…MediumSingle correct
8 Apr 2023, Shift 2 · Q16Let the vectors $\vec{u}_1 = \hat{i} + \hat{j} + a\hat{k}$ , $\vec{u}_2 = \hat{i} + b\hat{j} + \hat{k}$ and…HardSingle 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.