   Chapter 12.2, Problem 29E

Chapter
Section
Textbook Problem

# If v lies in the first quadrant and makes an angle π/3 with the positive x-axis and | v | = 4, find v in component form.

To determine

To find: The component form of vector v.

Explanation

Given:

The magnitude of vector v (|v|) as 4 and the value of angle with positive x-axis as π3 .

Definition:

Plotting a triangle of vector:

Consider a two-dimensional vector a as ai+bj and hence xy-plane is used to plot the vector. Consider x-axis as i-component of vector and y-axis as j-component of vector. Plot the point (a,b) in xy-plane. Connect the vector point and origin to line and draw a perpendicular line on x-axis from the point. Therefore, a right angle triangle is made using a vector.

Formula:

Write the expression for cosθ of right angle triangle.

Write the expression for sinθ of right angle triangle.

sinθ=oppositesidehypotenuse (2)

Consider the formula for component form for vector v.

v=v1,v2 (3)

According to definition, Consider x-axis as i-component of vector and y-axis as j-component of vector. Plot the point (v1,v2) in xy-pane. Connect the vector point and origin to line and draw a perpendicular line on x-axis from the point. Therefore, a right angle triangle is made using a vector.

The sketch of vector v=v1,v2 is shown in Figure 1.

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