Question

How do you find u=6w+2z given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?

Answer 1

`u=[18,36,2]`

Explanation:

Find `u=6w+2z` where `w=[2,6,-1]` and `z=[3,0,4]`.

This is essentially a substitution problem and you need to remember that when adding vectors you add corresponding components. So `[a_1,a_2,a_3]+[b_1,b_2,b_3]=[a_1+b_1, a_2+b_2, a_3+b_3]`

`6w=[6(2), 6(6), 6(-1)]=[12,36,-6]`.
`2z=[2(3),2(0),2(4)]=[6,0,8]`.

`u=6w+2z`
`u=[12,36,-6]+[6,0,8]=[18,36,2]`

Answer 2

`bb ul u = << 18,36,2 >>`

Explanation:

We have:

`bb ul v = << 4,-3,5 >>`
`bb ul w =<< 2,6,-1 >>`
`bb ul z =<< 3,0,4 >>`

Then, to compute `bb ul u`, we just scale the individual vectors and add the individual components, thus:

`bb ul u = 6bb ul w+2bb ul z`
`\ \ \ = 6<< 2,6,-1 >> + 2<< 3,0,4 >>`
`\ \ \ = << 6*2,6*6,6*(-1) >> + << 2*3,2*0,2*4 >>`
`\ \ \ = << 12,36,-6 >> + << 6,0,8 >>`
`\ \ \ = << 12+6,36+0,-6+8 >>`
`\ \ \ = << 18,36,2 >>`

Note that `bb ul v` is superfluous to the question.