Question

Compute the indicated quantities when
u = <2,1,-3>
v = <4,0,1>
w = <-2,6,5>

* = dot product
x = cross product
(u x v)*w
I got i-14j-4k for (u x v)
How do I get the the cross product with w?
My calculator says -106 but I got -2i-84j-20k

Answer 1

Yeah, for (uxv)*w, don't follow what your calculator says.
You computed the cross product. Now you're just multiplying that vector by a scalar multiple, w.

Answer 2

So is my answer right? I just multiplied
i *-2 = -2i
6*-14 = -84j
-4*5 = -20k
thus, -2i-84j-20k

Answer 3

OH. Whoops, I didn't see that 'w' was a vector.
There is no 'multplication' of two vectors, just dot product and cross product. I'm not sure. :3

Answer 4

Maybe they meant the magnitude of vector w?

Answer 5

well then what would be the dot product of, lets say r=<i-14j-4k> and w = <-2,6,5>:
r*w

Answer 6

Do you know how to calculator dot product?

Answer 7

calculate*?

Answer 8

yeah its would be like t=<x1,x2,x3> and r=<y1,y2,y3>
t*r = x1y1+x2y2+x3y3

Answer 9

Exactly. Same thing in this case. You found a vector from a cross product. You dot product the result with another vector.

Answer 10

well that's how I got -2i-84j-20k
I just want to make sure that that is correct. Here is my work:
i-14j-4k dot product with w = <-2,6,5>
i *-2 = -2i
-14j*6 = -84j
-4k*5 = -20k

Answer 11

i-14j-4k comes from u x v

Answer 12

WHOA. The result of a dot product is scalar, not a vector.

Answer 13

so u x v should stay scalar?

Answer 14

You said it. We're adding up the products of each corresponding component. Not making a new vector.

Answer 15

No, r.w is scalar.
The cross product yields another vector.

Answer 16

I should've said the result of a dot product is scalar.

Answer 17

Ok I see, so the calculator was right, its -106.
I thought I would get a vector.
-2-84-20=-106

Answer 18

Yeah, that would be correct if they are actually looking for the dot product.

Answer 19

So anytime I do a dot product, the answer will always be scalar?

Answer 20

Yes m8. B)

Answer 21

what about when I do a cross product? Will I always get a vector?

Answer 22

Yes yes m8. B)
And graphically, the result of the cross product will be perpendicular to the two vectors doing the product.

Answer 23

Ok thx, that's the part I didn't know; that cross products equal vectors and dot products equal scalars

Answer 24

YESH.