The tangent of the angle between a diagonal of a cube and th... | MATH - PLANE | SolveeIt | Solveeit

Today, August 23

Question

The tangent of the angle between a diagonal of a cube and the diagonal of a face (which meets the former) is-

A

$\frac { 1 } { \sqrt { 3 } }$

B

$\frac { 1 } { \sqrt { 2 } }$

C

$\frac { 1 } { 3 }$

D

$\sqrt { \frac { 2 } { 3 } }$

Answer

$\frac { 1 } { \sqrt { 2 } }$

Explanation

Solution

dr's of AL a, – a, – a

dr's of AP a, a, a

q between AL and AP

cos q = = – $\sqrt { \frac { 2 } { 3 } }$

Ž tan q = $\frac { 1 } { \sqrt { 2 } }$