Chapter 9: Q. 53 (page 603)

Find a vector $v$ whose magnitude is $4$ and whose component
in the $i$ direction is twice the component in the $j$ direction.

Short Answer

Expert verified

The vector is $\frac{8}{\sqrt{5}} i + \frac{4}{\sqrt{5}} j$

Step by step solution

Step 1. Given information

According to the question the vector will be,

$v = 2 x i + x j$

Step 2. Magnitude of the vector

The magnitude of the vector $v = 2 x i + x j$ is $\sqrt{4 x^{2} + x^{2}} = 4$

$\sqrt{5 x^{2}} = 4 5 x^{2} = 16 x^{2} = \frac{16}{5} x = \frac{4}{\sqrt{5}}$

Step 3. Required vector

Now the vector will be

$v = 2 x i + x j v = 2 (\frac{4}{\sqrt{5}}) i + \frac{4}{\sqrt{5}} j v = \frac{8}{\sqrt{5}} i + \frac{4}{\sqrt{5}} j$

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Find a vector $v$ whose magnitude is $4$ and whose component
in the $i$ direction is twice the component in the $j$ direction.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Magnitude of the vector

Step 3. Required vector

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Find a vector vwhose magnitude is 4and whose componentin the idirection is twice the component in the jdirection.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Magnitude of the vector

Step 3. Required vector

One App. One Place for Learning.

Most popular questions from this chapter

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Find a vector $v$ whose magnitude is $4$ and whose component
in the $i$ direction is twice the component in the $j$ direction.