Question

How do you find `u=3/4v-w` given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?

Answer 1

`u = <<0, - frac(9)(4), - frac(1)(4)>>`

Explanation:

We have: `u = frac(3)(4) v - w`

First, let's substitute the vector expressions in place of `v` and `w`:

`Rightarrow u = frac(3)(4) (4 i - 3 j + 5 k) - (3 i + 0 j + 4 k)`

Expanding the parentheses:

`Rightarrow u = 3 i - frac(9)(4) j + frac(15)(4) k - 3 i - 0 j - 4 k`

Collecting like vector components:

`Rightarrow u = 0 i - frac(9)(4) j - frac(1)(4) k`

`therefore u = <<0, - frac(9)(4), - frac(1)(4)>>`

Therefore, the vector `u` is simplified to `<<0, - frac(9)(4), - frac(1)(4)>>`.