Question

let vector u={-1,-1}. find vector v such that u*v=-6 and |v|= sqrt(18).

Answer 1

Is the * supposed to mean "dot product?"

Answer 2

i think so. im looking through the textbook to find out.

Answer 3

Let v = (x,y). You're given that u = (-1,-1). The dot product of the two vectors is
\[\begin{align*}u\cdot v&=(-1)x+(-1)y\\-6&=-x-y\\6&=x+y\end{align*}\]
The length of v, or |v|, is said to be √18, so you have
\[\begin{align*}|v|&=\sqrt{(x)^2+(y)^2}\\\sqrt{18}&=\sqrt{x^2+y^2}\\
18&=x^2+y^2\end{align*}\]
Think you can solve the system?

Answer 4

|v|=18, x=3, y=3

Answer 5

That's right

Answer 6

so vector v={3,3}?

Answer 7

Yes.

Answer 8

thanks