Examples for Vector algebra

Example 1

Draw the vectors a + b and a - b in the diagrams below.

Solution

Example 2

Express the unknown vector v in terms of a and b.

Solution

• v = b - a.
• v = a - b.

Example 3

Express the vector v in terms of a, b and c.

Solution

Example 4

Simplify the following expressions.

• a + 2b + 3(b - 5a)
• a - 7b + 7(b - a)
• 2a - 3b + c -(a - 3b)

Solution

• -15a + b
• -6a
• a - 2b + c