Find the length and direction (when defined) of u × v.
-u = 3i + 5j - 3k, v = -6i - 10j + 6k
A) $\sqrt { 215 } ; \frac { 1 } { \sqrt { 215 } } ( - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k } )$
B) $\sqrt { 129 } ; \frac { 1 } { \sqrt { 129 } } ( - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k } )$
C) $0 ; - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k }$
D) 0 ; no direction

Question

Find the length and direction (when defined) of u × v.
-u = 3i + 5j - 3k, v = -6i - 10j + 6k 
A) $\sqrt { 215 } ; \frac { 1 } { \sqrt { 215 } } ( - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k } )$
B) $\sqrt { 129 } ; \frac { 1 } { \sqrt { 129 } } ( - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k } )$
C) $0 ; - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k }$
D) 0 ; no direction

Quizplus · Accepted Answer

The cross product of two parallel or anti-parallel vectors is zero, which means the vector resulting from the cross product has a magnitude of 0 and no defined direction. In this case, $u$ and $v$ are anti-parallel (they are scalar multiples of each other, with $v = -2u$), so their cross product is a zero vector, which has no direction.

Find the Length and Direction (When Defined) of U × 215;1215(−3i−5j+3k)\sqrt { 215 } ; \frac { 1 } { \sqrt { 215 } } ( - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k } )215​;215​1​(−3i−5j+3k)

Find the Length and Direction (When Defined) of U × $\sqrt { 215 } ; \frac { 1 } { \sqrt { 215 } } ( - 3 \mathbf { i } - 5 \mathbf { j } + 3 \mathbf { k } )$