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Chapter 3: Q. 15 (page 77)

Let A = 4i - 2j, B = -3i + 5j, and E = 2A + 3B.
a. Write vector E in component form.
b. Draw a coordinate system and on it show vectors A, B, and E .
c. What are the magnitude and direction of vector E?

Short Answer

Expert verified

a) The vector E is -i^+11j^

b) The vectors are drawn in the coordinate system

c) The magnitude of the vector E is 11.04

Step by step solution

01

Write the given information

A鈫�=4i^-2j^,B鈫�=-3i^+5j^E鈫�=2A鈫�+3B鈫�

02

 Step 2: a) To determine vector E

The vector E is given by;
E鈫�=2A鈫�+3B鈫�E鈫�=2(4i^-2j^)+3(-3i^+5j^)E鈫�=8i^-4j^-9i^+15j^E鈫�=-i^+11j^
Thus, the vector E is-i^+11j^

03

b) To draw the vectors in the coordinate system 

The vectors A, B, and E are shown below in the coordinate system

04

c) To determine the magnitude of E

The vector E is given by -i^+11j^
The magnitude of the vector is given by

E鈫�=12+112=1+121=122=11.04
Thus, the magnitude of the vector E is 11.04

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