The Dot Product Question?

Question

In the following exercise, use the given vectors to find v X w and v X v.

v = -8i – 3j. w = -10i – 5j

Answer 1

Vector product is X, not dot product.
Then you would have to solve

vXw = i j k
-8 -3 0
-10 -5 0 = i(0)-j(0)+k(40-30) = -10k

if you meant the dot product by X, it would be an easier problem:

v X w = (-8)*(-10) + (-3)*(-5) = 80 +15=95

Answer 2

The symbol x means cross product, not dot product.
First, v x v = 0. Next,
imbed v and w in 3 space by making the 3rd component 0.
Then v x w is the determinant
| i j k|
| -8 -3 0|
| -10 -5 0|
So v x w = (40-30)k = 10k.

Answer 3

Hi,

v x w = (-8)(-10) + (-3)(-5) = 80 + 15 = 95

v x v = (-8)(-8) + (-3)(-3) = 64 + 9 = 73

I hope that helps!! :-)