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

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Answer 1 · 2017-06-06T21:30:01

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

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 $<<0, - frac(9)(4), - frac(1)(4)>>$ .

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