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\|=√(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=√(45)`, we have
`\|\mathbf u\|=\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`