Find the length and direction (when defined) of u × v.
-u = 2i + 2j - k, v = -i + k
A) $3 ; \frac { 2 } { 3 } \mathrm { i } - \frac { 1 } { 3 } \mathrm { j } + \frac { 2 } { 3 } \mathrm { k }$
B) $9 ; \frac { 2 } { 9 } \mathrm { i } + \frac { 1 } { 9 } \mathrm { j } - \frac { 2 } { 9 } \mathrm { k }$
C) $3 ; \frac { 2 } { 3 } \mathrm { i } + \frac { 1 } { 3 } \mathrm { j } - \frac { 2 } { 3 } \mathrm { k }$
D) $9 ; \frac { 2 } { 9 } \mathrm { i } - \frac { 1 } { 9 } \mathrm { j } + \frac { 2 } { 9 } \mathrm { k }$

Question

Find the length and direction (when defined) of u × v.
-u = 2i + 2j - k, v = -i + k 
A) $3 ; \frac { 2 } { 3 } \mathrm { i } - \frac { 1 } { 3 } \mathrm { j } + \frac { 2 } { 3 } \mathrm { k }$
B) $9 ; \frac { 2 } { 9 } \mathrm { i } + \frac { 1 } { 9 } \mathrm { j } - \frac { 2 } { 9 } \mathrm { k }$
C) $3 ; \frac { 2 } { 3 } \mathrm { i } + \frac { 1 } { 3 } \mathrm { j } - \frac { 2 } { 3 } \mathrm { k }$
D) $9 ; \frac { 2 } { 9 } \mathrm { i } - \frac { 1 } { 9 } \mathrm { j } + \frac { 2 } { 9 } \mathrm { k }$

Quizplus · Accepted Answer

u × v = (2i + 2j - k) × (-i + k) = -2i - 2j - 2k|u × v| = √((-2)² + (-2)² + (-2)²) = √12 = 2√3u × v / |u × v| = (-2i - 2j - 2k) / 2√3 = (-1/√3)i - (1/√3)j - (1/√3)k

Find the Length and Direction (When Defined) of U × 3;23i−13j+23k3 ; \frac { 2 } { 3 } \mathrm { i } - \frac { 1 } { 3 } \mathrm { j } + \frac { 2 } { 3 } \mathrm { k }3;32​i−31​j+32​k

Find the Length and Direction (When Defined) of U × $3 ; \frac { 2 } { 3 } \mathrm { i } - \frac { 1 } { 3 } \mathrm { j } + \frac { 2 } { 3 } \mathrm { k }$