Engineering Mechanics: Statics
8th Edition
ISBN: 9781118807330
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY

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Textbook Question
Chapter 1, Problem 1P

Determine the angles made by the vector V = 36 i + 15 j with the positive x- and y-axes. Write the unit vector n in the direction of V.

To determine

The angle made by the given vector with the positive x and y axes.

The unit vector n in the direction of V.

The angle made by the given vector with the positive x is 157.38° and y axes is 67.38°.

The unit vector n in the direction of V is 0.923i+0.385j.

Explanation of Solution

Given information:

The given vector is V=36i+15j.

Write the expression for the magnitude of vector.

|V|=a2+b2   ........(I)

Here, the magnitude of vector is |V|, the component of vector in x direction is a, and the component of vector in y direction is b.

Write the expression for angle made by vector with positive x axis.

cosθx=a|V|   ........(II)

Here, the angle made by vector with positive x axis. is θx.

Write the expression for angle made by vector with positive y axis.

cosθy=b|V|   ........(II)

Here, the angle made by vector with positive y axis. is θy.

Write the expression for the unit vector.

n=V|V|   ........(III)

Here, the unit vector in the direction of V is n.

Calculation:

Substitute 36 for a and 15 for b in Equation (I).

|V|=(36)2+(15)2=1296+225=39

Substitute 36 for a and 39 for |V| in Equation (II).

cosθx=3639θx=cos1(3639)=157.38°

Substitute 15 for b and 39 for |V| in Equation (III).

cosθy=1539θy=cos1(1539)=67.38°

Substitute 36i+15j for V and 39 for |V| in Equation (IV).

n=36i+15j39=0.923i+0.385j

Conclusion:

The angle made by the given vector with the positive x is 157.38° and y axes is 67.38°.

The unit vector n in the direction of V is 0.923i+0.385j.

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