Question

Help with vectors?

Answer 1

For vector u and v, is it true that (u-v)(u-v) = u^2-2uv+v^2?

Answer 2

i HAVE NO IDEA

Answer 3

what is uv? there is no vector multiplication.

Answer 4

@amonaroll32 The question has to specify the vector multiplication dot or cross product.

Answer 5

Um this is how the exact question was phrased:
For any two numbers a and b, the product of a-b times itself is equal to a^2-2ab+b^2. Does this familiar algebraic result hold for dot product of a vector u-v ith itself? In other words, is it true that (u-v)(u-v)=u^2-2uv+v^2? Justify your conclusion, trying not to express vectors u and v in component form.

Answer 6

u^2 or v^2 does not make sense.

(u - v) (u - v) = ||u||^2 + 2uv + ||v|||^2

Answer 7

of course, (u-v) (u-v) means (u-v) dot (u-v) in this context. and uv means u dot v

Answer 8

\[
(u-v)\cdot(u-v) = u\cdot(u-v)-v\cdot(u-v) = u\cdot u-u\cdot v-v\cdot u+v\cdot v
\]

Answer 9

Due to the distributive property and the commutative property, it works.

Answer 10

it must be the dot and it works

Answer 11

@wio is right. I'll just add that the dot product of u and u is the square of the magnitude of u

Answer 12

Ok thanks!