Q. 54 Find a vector v whose magnitude ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 54 (page 603)

Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction.

Short Answer

Expert verified

Vector v is $\frac{3}{\sqrt{2}} \overset{鈬赌}{i} + \frac{3}{\sqrt{2}} \overset{鈬赌}{j}$

Step by step solution

Step. 1 Given

|v| = 3 and,

angle of the vector from both $\overset{鈬赌}{i} a n d \overset{鈬赌}{j}$ directions is same suppose that angle be $胃$ .

Step. 2 Vector representation

Now, As we know the general form of a vector is,

$\overset{鈬赌}{v} = r (\cos (胃) \overset{鈬赌}{i} + \sin (胃) \overset{鈬赌}{j})$

where, r is the magnitude of the vector i.e., distance from the origin and $胃$ is the angle of that vector from x-axis or $\overset{鈬赌}{i}$ direction.

Now, as magnitude in the question is given itself as 3. So,

role="math" localid="1646738176258" $r = 3$ .

So,

$\overset{鈬赌}{v} = 3 (\cos (胃) \overset{鈬赌}{i} + \sin (胃) \overset{鈬赌}{j})$

Step. 3 Final solution

Now, we have left with only $胃$ ,

So, as it is given that it makes equal angles with and we know these directions are mutually perpendicular thatswhy

$胃 = 45 掳 o r \frac{蟺}{4},$

Finally,

$\overset{鈬赌}{v} = 3 (\cos (\frac{蟺}{4}) \overset{鈬赌}{i} + \sin (\frac{蟺}{4}) \overset{鈬赌}{j}), \overset{鈬赌}{v} = 3 (\frac{\overset{鈬赌}{i}}{\sqrt{2}} + \frac{\overset{鈬赌}{j}}{\sqrt{2}}), \overset{鈬赌}{v} = \frac{3}{\sqrt{2}} \overset{鈬赌}{i} + \frac{3}{\sqrt{2}} \overset{鈬赌}{j} .$

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91影视

Find a vector v whose magnitude is 3 and whose component in the i direction is equal to the component in the j direction.

Short Answer

Step by step solution

Step. 1 Given

Step. 2 Vector representation

Step. 3 Final solution

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