GATE 2021 CS (CS2) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

If θ is the angle between the longest diagonal of a cube and any edge, find cos θ.

1/2
$1/\sqrt3$
$1/\sqrt2$
$\sqrt3/2$

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Correct answer: (B) $1/\sqrt3$

Explanation

For side length a, take the space-diagonal vector (a,a,a) and an edge vector (a,0,0). Their dot product is a² and the product of their lengths is a√3×a. Hence cos θ=1/√3, B.

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