Question

The angle subtended by the vector A = `5hat"i" + 3hat"j" + 12hat"k"` with the X-axis is ______.

Options

• `cos^-1 (3/13)`

• `sin^-1 (3/13)`

• `sin^-1 (4/13)`

• `cos^-1 (4/13)`

Answer 1

The angle subtended by the vector A = `5hat"i" + 3hat"j" + 12hat"k"` with the X-axis is `underline(cos^-1 (4/13))`.

Explanation:

Given, A = `4hat"i" + 3hat"j" + 12hat"k"`

Also, A = A_x + A_y + A_z

`=> "A"_x = 4`

The angle subtended by vector A with X-axis is

`cos phi = "A"/|"A"| = 4/(sqrt(4^2 + 3^2 + 12^2))`

cos Φ = \[\frac{4}{13}\]

Φ = `cos^-1 (4/13)`