Question

Assume that u⋅v=5, ∥u∥=10, and ∥v∥=7.

What is the value of 3u⋅(9u−9v)?

Answer 1

Answer: 3u⋅(9u−9v) = 285

Explanation:

We can start by using the distributive property for the dot product:

3u⋅(9u−9v) = 3u⋅9u - 3u⋅9v

We also know that the dot product of two vectors u and v is u⋅v = ∥u∥∥v∥cos(θ), where θ is the angle between vectors u and v. Therefore,

u⋅v = 5 = 107cos(θ)

So we can write:

cos(θ) = 5/(10*7) = 1/14

Then we can use this value to find the dot product of u and v.

3u⋅9u = 3 * (10^2) = 300

3u⋅9v = 3 * (10)(7)(1/14) = 15

So the final answer is:

3u⋅(9u−9v) = 300 - 15 = 285

Explanation: By using the distributive property and the dot product definition, it was possible to find the dot product of 3u⋅9u and 3u⋅9v. By subtracting the latter from the former, we obtained the final answer of 285.