Chapter 9: Q. 55 (page 603)

If $\overset{⇀}{v} = 2 \overset{⇀}{i} - \overset{⇀}{j}$ and $\overset{⇀}{w} = x \overset{⇀}{i} + 3 \overset{⇀}{j}$ , find all numbers x for which $|\overset{⇀}{v} + \overset{⇀}{w}| = 5$ .

Short Answer

Expert verified

There will be two such values of x which are $\sqrt{21} - 2 a n d - \sqrt{21} - 2$

Step by step solution

Step. 1 Given

$\overset{⇀}{v} = 2 \overset{⇀}{i} - \overset{⇀}{j}$ and $\overset{⇀}{w} = x \overset{⇀}{i} + 3 \overset{⇀}{j}$

Step. 2 Magnitude of a vector

Firstly, we need to find the vector $\overset{⇀}{v} + \overset{⇀}{w}$ ,

so,

$\overset{⇀}{v} + \overset{⇀}{w} = (2 \overset{⇀}{i} - \overset{⇀}{j}) + (x \overset{⇀}{i} + 3 \overset{⇀}{j}) \overset{⇀}{v} + \overset{⇀}{w} = (2 \overset{⇀}{i} + x \overset{⇀}{i}) + (- \overset{⇀}{j} + 3 \overset{⇀}{j}) \overset{⇀}{v} + \overset{⇀}{w} = (x + 2) \overset{⇀}{i} + 2 \overset{⇀}{j}$

we get the vector whose magnitude is given i.e., 5

So, $|\overset{⇀}{v} + \overset{⇀}{w}| = 5 \sqrt{{(x + 2)}^{2} + {(2)}^{2}} = 5$

Step. 3 Final solution

Now we have one equation in one variable. Solve it for x,

$\sqrt{{(x + 2)}^{2} + 4} = 5$ ,

Squaring both sides we get,

${(x + 2)}^{2} + 4 = 25 {(x + 2)}^{2} = 21$ ,

Taking square root both sides we get,

$(x + 2) = \pm \sqrt{21}, x = \pm \sqrt{21} - 2,$

So,

$x = \sqrt{21} - 2 o r x = - \sqrt{21} - 2$

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If $\overset{⇀}{v} = 2 \overset{⇀}{i} - \overset{⇀}{j}$ and $\overset{⇀}{w} = x \overset{⇀}{i} + 3 \overset{⇀}{j}$ , find all numbers x for which $|\overset{⇀}{v} + \overset{⇀}{w}| = 5$ .

Short Answer

Step by step solution

Step. 1 Given

Step. 2 Magnitude of a vector

Step. 3 Final solution

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If v⇀=2i⇀-j⇀and w⇀=xi⇀+3j⇀, find all numbers x for which v⇀+w⇀=5.

Short Answer

Step by step solution

Step. 1 Given

Step. 2 Magnitude of a vector

Step. 3 Final solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Discrete Mathematics

Mechanics Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

If $\overset{⇀}{v} = 2 \overset{⇀}{i} - \overset{⇀}{j}$ and $\overset{⇀}{w} = x \overset{⇀}{i} + 3 \overset{⇀}{j}$ , find all numbers x for which $|\overset{⇀}{v} + \overset{⇀}{w}| = 5$ .