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

2 Answers
turksvids
Dec 17, 2017

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]

Steve M
Dec 17, 2017

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.

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