Question #200625

Let ~u =< 3, −1, −2 >, ~v =< −1, 0, 2 > and w~ =< −6, 1, 4 >.

Compute the expressions below.

(2.1) ~v + 3w~

(2.2) 3~u − 2~v

(2.3) −(~v + 3~u).


1
Expert's answer
2021-06-06T15:41:51-0400

(2.1)


v+3w=1+3(6),0+3(1),2+3(4)\vec v+3\vec w=\langle-1+3(-6), 0+3(1), 2+3(4)\rangle

v+3w=19,3,14\vec v+3\vec w=\langle-19, 3, 14\rangle


(2.2)


3u2v=3(3)2(1),3(1)2(0),3(2)2(2)3\vec u-2\vec v=\langle3(3)-2(-1), 3(-1)-2(0), 3(-2)-2(2)\rangle

3u2v=11,3,103\vec u-2\vec v=\langle11, -3, -10\rangle


(2.3)


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

(v+3u)=8,3,4-(\vec v+3\vec u)=\langle-8, 3, 4\rangle


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