Which graph shows vector u plus vector v for the given vectors u and v ?
Answer
A
Image with description On a coordinate plane, vector u has origin (0, 0) and terminal point (1, 4), vector u + v has origin (0, 0) and terminal point (1, negative 6), vector v has origin (0, 0) and terminal point (2, negative 2).
B
Image with description On a coordinate plane, vector u has origin (0, 0) and terminal point (1, 4), vector u + v has origin (0, 0) and terminal point (3, 6), vector v has origin (0, 0) and terminal point (2, negative 2).
C
Image with description On a coordinate plane, vector u has origin (0, 0) and terminal point (1, 4), vector u + v has origin (0, 0) and terminal point (negative 1, 6), vector v has origin (0, 0) and terminal point (2, negative 2).
D
Image with description On a coordinate plane, vector u has origin (0, 0) and terminal point (1, 4), vector u + v has origin (0, 0) and terminal point (3, 2), vector v has origin (0, 0) and terminal point (2, negative 2).
Explanation
Add the vectors by adding their corresponding components: u = (1, 4) and v = (2, −2), so u + v = (1 + 2, 4 + (−2)) = (3, 2). The graph with terminal point (3, 2) is choice C.
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