Question

Given the vectors u= <2, 1> and v= <5, 4>, determine the components of a vector represented by 2u - 3v

A.) <14, 15>

B.) <-6, -9>

C.) <-11, -10>

D.) <19, 14>

Answer 1

C.) <-11, -10>

Explanation:

Let's define how to work with vectors.

For two vectors:

V = <a, b>

W = <c, d>

The product of a scalar k and a vector is given by:

k*V = k*<a, b> = <k*a, k*b>

And the sum (or difference) of two vectors is given by:

V ± W = <a, b> ± <c, d> = <a ± c, b ± d>

Now that we know this, we can solve the problem.

Here we have the vectors:

u = <2, 1>

v = <5, 4>

then:

2u - 3*v = 2*<2, 1> - 3*<5, 4>

= <2*2, 2*1> - <3*5, 3*4>

= <4, 2> - <15, 12>

= <4 - 15, 2 - 12>

= < -11, -10>

Then the correct option is C.