Chapter 12.2, Problem 29E

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8th Edition

James Stewart

ISBN: 9781305266643

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**
*x*-axis as

**Definition:**

**Plotting a triangle of vector:**

Consider a two-dimensional vector **a** as
*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
*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

Write the expression for

Consider the formula for component form for vector **v**.

According to definition, Consider *x*-axis as **i**-component of vector and *y*-axis as **j**-component of vector. Plot the point
*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

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