Question

Can someone check and see if I got the right answer on these problems

Answer 1

(1) is correct. $\mathbf u\cdot\mathbf v=(-14)(0)+(8)(11)=0+88=88$

(2) is correct. I assume you just computed the dot product as above, but another way to do it is to notice that $\mathbf v\cdot\mathbf v=\|\mathbf v\|^2$ (that is, the dot product of a vector with itself is the square of its magnitude). Then since $\|\mathbf v\|=\sqrt{1^2+2^2}=\sqrt5$, we have $\mathbf v\cdot\mathbf v=\|\mathbf v\|^2=5$.

(3) is not correct. Since $\mathbf u\cdot\mathbf u=\|\mathbf u\|^2=\sqrt{45}$, we have $\|\mathbf u\|=\sqrt{\sqrt{45}}$.

(4) is correct.

$2\mathbf u\cdot\mathbf v=2(\mathbf u\cdot\mathbf v)=2((-3)(1)+(6)(2))=2(-3+12)=2(9)=18$