Determine the values of $c$ such that $\| c \mathbf { u } \| = 6$, where $\mathbf { u } = 6 \mathbf { i } + 5 \mathbf { j } + 5 \mathbf { k }$.
A) $c = \pm 6$
B) $c = \pm \frac { 3 \sqrt { 86 } } { 43 }$
C) $c = \pm \frac { \sqrt { 86 } } { 6 }$
D) $c = \pm \frac { 1 } { 6 }$
E) $c = \pm \frac { \sqrt { 86 } } { 86 }$

Question

Quizplus · Accepted Answer

The norm of a vector is given by the square root of the sum of the squares of its components. So, we have$$\| c \mathbf { u } \| = \sqrt{c^2(6)^2 + c^2(5)^2 + c^2(5)^2} = \sqrt{86c^2}.$$Setting this equal to 6, we get$$86c^2 = 36 \Rightarrow c^2 = \frac{36}{86} \Rightarrow c = \pm \frac{3\sqrt{86}}{43}.$$

Determine the Values Of ccc Such That ∥cu∥=6\| c \mathbf { u } \| = 6∥cu∥=6

Determine the Values Of $c$ Such That $\| c \mathbf { u } \| = 6$