Question

Two vectors and have the components, in meters, ax = 6.91, ay = 1.45, bx = 2.45, by = 7.02. (a) find the angle between the directions of and . there are two vectors in the xy plane that are perpendicular to and have a magnitude of 8.28 m. one, vector , has a positive x component and the other, vector , a negative x component. what are (b) the x component and (c) the y component of , and (d) the x component and (e) the y component of vector ?

Answer 1

We are given
ax = 6.91
ay = 1.45

bx = 2.45
by = 7.02

So,
tan a→ = 1.45/6.91 = 0.2098 = ma
tan b→ = 7.02/2.45 = 2.8653 = mb

To get the angle between the two
tan θ = (mb - ma)/(1 + ma mb)
tan θ = (2.8653 - 0.2098) / (1 + (2.8653) (0.2098) )
θ = 58.91°
The x component is
x = 8.28 cos 58.91 = 4.28 m
The y component is
y = 8.28 sin 58.91 =  7.09 m