Two vectors lying in the xy plane are given by the equations and . The value of is:
A)19
B)(-11 )
C)(-19 )
D)11
E)10

Question

Two vectors lying in the xy plane are given by the equations  and  . The value of  is:
A)19 
B)(-11 ) 
C)(-19 ) 
D)11 
E)10

Quizplus · Accepted Answer

We can find the dot product of the two given vectors:
(11, 8) · (10, -5) = 11(10) + 8(-5) = 90
The magnitude of the first vector is:
√((11)² + (8)²) = √(185)
Therefore, the value of cosθ is:
cosθ = 90/(√(185)*√(125)) ≈ 0.79819
θ ≈ 37.326°
Finally, the scalar projection of the second vector onto the first vector is:
||v2||cosθ ≈ 19.

Two Vectors Lying in the Xy Plane Are Given by the Equations