Express the vector as a product of its length and direction.
-5i + 10j + 10k
A) $15 \left( \frac { 1 } { 45 } \mathrm { i } + \frac { 2 } { 45 } \mathrm { j } + \frac { 2 } { 45 } \mathrm { k } \right)$
B) $15 ( 5 \mathbf { i } + 10 \mathbf { j } + 10 \mathbf { k } )$
C) $15 ( \mathbf { i } + \mathbf { j } + \mathbf { k } )$
D) $15 \left( \frac { 1 } { 3 } \mathrm { i } + \frac { 2 } { 3 } \mathrm { j } + \frac { 2 } { 3 } \mathrm { k } \right)$

Question

Express the vector as a product of its length and direction.
-5i + 10j + 10k 
A) $15 \left( \frac { 1 } { 45 } \mathrm { i } + \frac { 2 } { 45 } \mathrm { j } + \frac { 2 } { 45 } \mathrm { k } \right)$
B) $15 ( 5 \mathbf { i } + 10 \mathbf { j } + 10 \mathbf { k } )$
C) $15 ( \mathbf { i } + \mathbf { j } + \mathbf { k } )$
D) $15 \left( \frac { 1 } { 3 } \mathrm { i } + \frac { 2 } { 3 } \mathrm { j } + \frac { 2 } { 3 } \mathrm { k } \right)$

Quizplus · Accepted Answer

To express the vector as a product of its length and direction, we first find the length or magnitude of the vector. 
Magnitude = sqrt(5^2+10^2+10^2) = sqrt(225) = 15
Next, we find the direction of the vector by dividing each component of the vector by its magnitude:
Direction = (5/15)i + (10/15)j + (10/15)k = (1/3)i + (2/3)j + (2/3)k
Therefore, the product of the length and direction is 15 times the direction vector, which is option D.

Express the Vector as a Product of Its Length and Direction