Question

Evaluate the expression.

r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1>

v ⋅ w

<-15, -27, -32>
0
17
<27, -18, 8>

Answer 1

\[r=5 \hat{i}+9 \hat{j}-4 \hat{k}\\v=3 \hat{i}+3 \hat{j}-8 \hat{k}\\w=9 \hat{i}-6 \hat{j}-\hat{k}\]
now simple dot product

Answer 2

\[v.w=(3 \hat{i}+3 \hat{j}-8 \hat{k}).(9 \hat{i}-6 \hat{j}-\hat{k})=(3*9-6*3+8)=17\]

Answer 3

got it?

Answer 4

\[used~these\\i*i=j*j=k*k=1\]