Example 3.3 The Sum of Two Vectors Find the sum of two vectors and lying in the

Question

Example 3.3 The Sum of Two Vectors
Find the sum of two vectors and lying in the xy plane and given by:

= (1.68 + 2.08) m and = (5.3 + -5.31) m
SOLVE IT
Conceptualize You can conceptualize the situation by drawing the vectors on graph paper.

Categorize We categorize this example as a simple substitution problem. Comparing this expression for with the general expression = Ax + Ay + Az, we see that Ax = 1.68 m and Ay = 2.08 m. Likewise, Bx = 5.3 m and By = -5.31 m.
Use the following equation to obtain the resultant vector :
= + = (1.68 + 5.3) m + (2.08 + -5.31) m
Evaluate the components of :
Rx = 6.98 m Ry = -3.23 m
Use the following equation to find the magnitude of :


= m
Find the direction of from the following equation:
tan ? =
Ry
Rx
=
-3.23 m
6.98 m
= -0.46
Your calculator likely gives the answer -24.83

Explanation / Answer

A = 1.01 i + 4.75 j

B = 2.79 i + 3.77 j

So, A + B = (1.01 + 2.79) i + (4.75 + 3.77) j

A + B = 3.80 i + 8.52 j

Thus, magnitude of (A+B) = (3.802 + 8.522) = 9.329

Thus, R = 9.329

Angle = atan(8.52/3.80) = 65.962 deg

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