Solve the problem.
-Find a vector of magnitude 11 in the direction of v = 5i - 12k.
A) $\frac { 11 } { 13 } ( 5 \mathbf { i } - 12 \mathbf { k } )$
B) $11 ( 5 \mathbf { i } - 12 \mathbf { k } )$
C) $11 ( \mathbf { i } - \mathbf { k } )$
D) $\frac { 1 } { 13 } ( 5 \mathbf { i } - 12 \mathbf { k } )$

Question

Solve the problem.
-Find a vector of magnitude 11 in the direction of v = 5i - 12k. 
A) $\frac { 11 } { 13 } ( 5 \mathbf { i } - 12 \mathbf { k } )$
B) $11 ( 5 \mathbf { i } - 12 \mathbf { k } )$
C) $11 ( \mathbf { i } - \mathbf { k } )$
D) $\frac { 1 } { 13 } ( 5 \mathbf { i } - 12 \mathbf { k } )$

Quizplus · Accepted Answer

To find a vector of magnitude 11 in the direction of v, we need to find a unit vector in the direction of v and then multiply it by 11. To find a unit vector in the direction of v, we need to divide v by its magnitude: 
$$\frac{v}{|v|} = \frac{5\mathbf{i}-12\mathbf{k}}{\sqrt{5^2+0^2+(-12)^2}} = \frac{5\mathbf{i}-12\mathbf{k}}{13}$$
Multiplying this unit vector by 11 gives:
$$11\cdot\frac{5\mathbf{i}-12\mathbf{k}}{13} = \frac{55\mathbf{i}-132\mathbf{k}}{13} = \frac{11}{13}(5\mathbf{i}-12\mathbf{k})$$
Therefore, the answer is (A).

Solve the Problem 1113(5i−12k)\frac { 11 } { 13 } ( 5 \mathbf { i } - 12 \mathbf { k } )1311​(5i−12k)

Solve the Problem $\frac { 11 } { 13 } ( 5 \mathbf { i } - 12 \mathbf { k } )$