Given the ordered pairs for the initial and terminal points of each vector, are the two vectors equivalent?
Given the ordered pairs for the initial and terminal points of each vector, are the two vectors equivalent?
1) \(\mathrm{Q}(1,1), \mathrm{R}(5,-3), \mathrm{A}(-5,0), \mathrm{B}(-1,-4)\)
\(\overrightarrow{\mathrm{QR}} \cdot \overrightarrow{\mathrm{AB}}\)
2) \(A(3,1), B(0,3), C(-4,2), D(-1,-1)\)
\(\overrightarrow{\mathrm{AB}} \cdot \overrightarrow{\mathrm{CD}}\)
Homework Answers
SOLUTION :
1.
—->
QR = (5 - 1) I + (- 3 - 1) j = 4 I - 4 j
—->
AB = (- 1 - (-5)) I + (-4 - 0) j = 4 I - 4 j
—> —>
Hence, QR = AB. (Equal) (ANSWER)
2.
—->
AB = (0 - 3) I + (3 - 1) j = - 3 I + 2j
—>
CD = (-1 - (-4)) I + (-1 - 2) j = 3 I - 3j
—> —>
So, AB ≠ CD. (Not equal) (ANSWER)
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Given the ordered pairs for the initial and terminal points of each vector, are the two vectors equivalent?
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