GATE CSE 2021 Set 2 Q3: Angle between the longest diagonal and an edge of a cube

If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, $\cos\theta =$

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

Show answer and explanation

Answer: B (official GATE 2021 final answer key)

Concept used: Angle between two vectors through the dot product.

First step: Take the diagonal $(1,1,1)$ and the edge $(1,0,0)$ of a unit cube: $\cos\theta = \dfrac{1}{\sqrt{3}\cdot 1}$ .

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key