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) $\mathbf { v } = \frac { 52 } { 5 } \sqrt { 5 } \mathbf { i } + \frac { 26 } { 5 } \sqrt { 5 } \mathbf { j } \quad$ or $\quad \mathbf { v } = - \frac { 52 } { 5 } \sqrt { 5 } \mathbf { i } - \frac { 26 } { 5 } \sqrt { 5 } \mathrm { j }$
B) $\mathbf { v } = \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j } \quad$ or $\quad \mathbf { v } = - \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } + \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$
C) $\mathbf { v } = - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { i } + \frac { 11 } { 10 } \sqrt { 10 } \mathbf { j } \quad$ or $\quad \mathbf { v } = \frac { 33 } { 10 } \sqrt { 10 } \mathbf { i } - \frac { 11 } { 10 } \sqrt { 10 } \mathbf { j }$
D) $\mathbf { v } = \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } + \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j } \quad$ or $\quad \mathbf { v } = - \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$

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) $\mathbf { v } = \frac { 52 } { 5 } \sqrt { 5 } \mathbf { i } + \frac { 26 } { 5 } \sqrt { 5 } \mathbf { j } \quad$ or $\quad \mathbf { v } = - \frac { 52 } { 5 } \sqrt { 5 } \mathbf { i } - \frac { 26 } { 5 } \sqrt { 5 } \mathrm { j }$
B) $\mathbf { v } = \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j } \quad$ or $\quad \mathbf { v } = - \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } + \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$
C) $\mathbf { v } = - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { i } + \frac { 11 } { 10 } \sqrt { 10 } \mathbf { j } \quad$ or $\quad \mathbf { v } = \frac { 33 } { 10 } \sqrt { 10 } \mathbf { i } - \frac { 11 } { 10 } \sqrt { 10 } \mathbf { j }$
D) $\mathbf { v } = \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } + \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j } \quad$ or $\quad \mathbf { v } = - \frac { 11 } { 10 } \sqrt { 10 } \mathbf { i } - \frac { 33 } { 10 } \sqrt { 10 } \mathbf { j }$

Quizplus · Accepted Answer

Given that the magnitude of $\mathbf{v}$ is 26 and the component in the i direction is twice the component in the j direction, we can set up the equation $|\mathbf{v}| = \sqrt{(2x)^2 + x^2} = 26$, where $x$ is the component in the j direction. Solving this equation gives $x = \frac{26}{5}\sqrt{5}$ and $2x = \frac{52}{5}\sqrt{5}$, which matches the components given in option A.

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

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