Answer
$<7, -1, -7>$
$<5, 1, -9>$
$10$
$<5/2, 2, -8>$
Work Step by Step
The question asks for $ u + v$, $u - v$, and $|u|$, $0.75u - 2 v$
Given $u = 6i - 8k$ and $v = i - j + k$
$u = <6, 0, -8>$ and $v = <1, -1, 1>$
$u + v = <6 + 1, 0 + (-1), -8 + 1> = <7, -1, -7>$
$u - v = <6 - 1, 0 - (-1), -8 - 1> = <5, 1, -9>$
$|u| = \sqrt {6^2 + 0^2 + (-8)^2} = \sqrt 100 = 10$
$0.75 u - 2v = <0.75 (6) - 2 (1), 0.75 (0) - 2(-1), 0.75 (-8) - 2 (1)>$
$= <5/2, 2, -8>$
