Question

1. A vector is defined as having magnitude of 15 m and a direction of East. Multiply this vector by the scalar value of –6. What is the resultant vector’s magnitude and direction?

A. 90 m East
B. 90 m West
C. -90 m East
D. -90 m West


2. What are the components of a vector C→ if its magnitude is 8.9 m/s and it makes an angle of –40° with the +x-axis?

A. Cx = –5.72 m/s, Cy = 6.82 m/s
B. Cx = 6.82 m/s, Cy = –5.72 m/s
C. Cx = –0.643 m/s, Cy = 0.766 m/s
D. Cx = 0.766 m/s, Cy = –0.643 m/s

Help!!!

Answer 1

#1 multiplying by a scalar does not change the direction
Just multiply each component by the scalar value

#2 as always, apply the usual conversion from rectangular to polar form:
x = r cosθ
y = r sinθ
In this case, r is just the length of the vector.

Answer 2

"A vector is defined as having magnitude of 15 m and a direction of East."
-----> [ 15, 0]
so -6[15,0] = [-90,0)]
how far is that point from the origin? 90
in which direction does it lie? west

"magnitude is 8.9 m/s and it makes an angle of –40° with the +x-axis"
----> [8.9cos(-40) , 8.9sin(-40) ] =

Answer 3

Thank you I got it now.