Solved Example & Practice Problems: Vector Addition

Solved Examples for Understanding

Example 1.8.1 

Solution :

Example 1.8.2 

Show that the vectors are parallel.

Solution: 

If two vectors are parallel, their cross product is zero.

Example 1.8.3 

Determine the unit vector along the line which orginates at the point (4, 1,-2) and passes through the point (2, 2, 6).

Solution: 

Example 1.8.4 

If vector

1) Find and the unit vector along it.

ii) Find the included angle between vector and the vector resulting from the cross product.

Solution: i)

Example 1.8.5 

With respect to origin (0, 0, 0), a point A is located at (-5, 2, 14). Specify the position of the point.

a) In terms of orthogonal components, b) In terms of directional cosine, and

c) In terms of unit vector.

Solution: 

a) The x, y, z components of A are

x =  - 5, y = 2, z = 14

Hence position vector of A can be written as

b) The direction cosines are

Example 1.8.6 

Solution:

Example 1.8.7 

Find is a unit vector.

Solution: 

Example 1.8.8

Find the angle between the forces A and B given as

Solution: 

Examples for Practice