Question

With given vectors u=<3,-1,-2> v=<-1,0,2> w=<-6,1,4> compute the expressions below
2.1 v+3w
2.2 u-2v
2.3 - (v+3u)

Answer 1

2.1

$$v+3w=\langle-1,0,2\rangle+3\langle-6,1,4\rangle$$

$$=\langle-1+3(-6), 0+3(1), 2+3(4)\rangle$$

$$=\langle-19,3, 14\rangle$$

2.2

$$u-2v=\langle3,-1,-2\rangle+(-2)\langle-1,0,2\rangle$$

$$=\langle3+(-2)(-1), -1+(-2)(0), -2+(-2)(2)\rangle$$

$$=\langle5,-1, -6\rangle$$

2.3

$$-(v+3u)=-(\langle -1,0,2\rangle+3\langle 3,-1,-2\rangle)$$

$$=-(\langle-1+3(3), 0+3(-1), 2+3(-2)\rangle)$$

$$=\langle-8,3, 4\rangle$$