Question

What is the angle, that Vector A =4i-8j+k makes with the coordinate axes (x, y, z)?​

Answer 1

Let b = 0i + 0j + zk ( here the components along x and y is zero because we have to find the angle between a and z-axis) and ¥ be the angle between them

As we know the relation that

a.b= ab cos¥

(3i - 4j + 5k). (0i +0j +zk) = | 3i - 4j + 5k | |0i +0j+ zk| cos ¥

5z = { (3)² +(-4)² +(5)² }½ { z²}½ cos ¥

5 z= √50 z cos ¥

5= 5√2 cos ¥

Cos¥ = 1/√2

Hence ¥ = 45°

So the vector a makes 45° with z-axis