Question

Let u = <7, -3>, v = <-9, 5>. Find 4u - 3v.

Answer 1

Given: u = <7, -3>  and v = <-9, 5>

To calculate:  4 u - 3 v

Now, we shall express the given value of u and v in vector form

u = 7 i - 3 j  and v = - 9 i + 5 j

So,        4 u - 3 v = 4 (7 i - 3 j ) - 3 (- 9 i + 5 j )

or,         4 u - 3 v = (28 i - 12 j ) - (- 27 i + 15 j )

or,         4 u - 3 v = (55 i - 27 j )

or,         4 u - 3 v = < 55 , - 27 >

Hence, the required value of 4 u - 3 v will be < 55 , - 27 >