Question

Find the angles made by the straight line passing through the points (1, -3, 2) and (4, -5, 1) with the coordinate axes.

Answer 1

Let the points are A(1, -3, 2) and B(4, -5, 1)

The straight line passing through these points corresponds to the VECTOR AB. So

Vector AB = ( 4 - 1, -5 - (-3) , 1 - 2 )

Vector AB = ( 3, -2 , - 1 )

Magnitude of Vector AB = $\sqrt{3^{2}+(-2)^{2} +(-1)^{2}} =\sqrt{14}$

Direction Cosines of AB = $[\frac{3}{\sqrt{14} },\frac{-2}{\sqrt{14} },\frac{-1}{\sqrt{14} }]$

ANGLES:

$With\ x-axis = Cos^{-1}\frac{3}{\sqrt{14} } =36.69degrees \\With\ y-axis = Cos^{-1}\frac{-2}{\sqrt{14} } = 122.31degrees \\With\ z-axis = Cos^{-1}\frac{-1}{\sqrt{14} } =105.50degrees$