Solve the problem.
-Find a vector v whose magnitude is 26 and whose component in the i direction is twice the component in the j direction.
A) $v = \frac { 52 } { 5 } \sqrt { 5 } i + \frac { 26 } { 5 } \sqrt { 5 } j \quad$ or $\quad \mathbf { v } = - \frac { 52 } { 5 } \sqrt { 5 } i - \frac { 26 } { 5 } \sqrt { 5 } \mathbf { j }$

B) $v = \frac { 11 } { 10 } \sqrt { 10 } i - \frac { 33 } { 10 } \sqrt { 10 } j \quad$ or $\quad v = - \frac { 11 } { 10 } \sqrt { 10 } i + \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$

C) $v = - \frac { 33 } { 10 } \sqrt { 10 } \mathrm { i } + \frac { 11 } { 10 } \sqrt { 10 } \mathrm { j } \quad$ or $\quad \mathbf { v } = \frac { 33 } { 10 } \sqrt { 10 } \mathrm { i } - \frac { 11 } { 10 } \sqrt { 10 } \mathrm { j }$

D) $v = \frac { 11 } { 10 } \sqrt { 10 } \mathrm { i } + \frac { 33 } { 10 } \sqrt { 10 } \mathrm { j } \quad$ or $\quad \mathbf { v } = - \frac { 11 } { 10 } \sqrt { 10 } \mathrm { i } - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$

Question

Solve the problem.
-Find a vector v whose magnitude is 26 and whose component in the i direction is twice the component in the j direction. 
A) $v = \frac { 52 } { 5 } \sqrt { 5 } i + \frac { 26 } { 5 } \sqrt { 5 } j \quad$ or $\quad \mathbf { v } = - \frac { 52 } { 5 } \sqrt { 5 } i - \frac { 26 } { 5 } \sqrt { 5 } \mathbf { j }$

B) $v = \frac { 11 } { 10 } \sqrt { 10 } i - \frac { 33 } { 10 } \sqrt { 10 } j \quad$ or $\quad v = - \frac { 11 } { 10 } \sqrt { 10 } i + \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$

C) $v = - \frac { 33 } { 10 } \sqrt { 10 } \mathrm { i } + \frac { 11 } { 10 } \sqrt { 10 } \mathrm { j } \quad$ or $\quad \mathbf { v } = \frac { 33 } { 10 } \sqrt { 10 } \mathrm { i } - \frac { 11 } { 10 } \sqrt { 10 } \mathrm { j }$

D) $v = \frac { 11 } { 10 } \sqrt { 10 } \mathrm { i } + \frac { 33 } { 10 } \sqrt { 10 } \mathrm { j } \quad$ or $\quad \mathbf { v } = - \frac { 11 } { 10 } \sqrt { 10 } \mathrm { i } - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$

Quizplus · Accepted Answer

Given that the magnitude of vector $v$ is 26 and the component in the $i$ direction is twice the component in the $j$ direction, we can set up the equation $|v| = \sqrt{(2j)^2 + j^2} = 26$, where $j$ is the component in the $j$ direction. Solving this equation gives us the components in the $i$ and $j$ directions as provided in choice A.

Solve the Problem v=5255i+2655jv = \frac { 52 } { 5 } \sqrt { 5 } i + \frac { 26 } { 5 } \sqrt { 5 } j \quadv=552​5​i+526​5​j

Solve the Problem $v = \frac { 52 } { 5 } \sqrt { 5 } i + \frac { 26 } { 5 } \sqrt { 5 } j \quad$