Two vectors a and b have the components, in meters, a 4.25, ay 1.97, b 1.72, by

Question

Two vectors a and b have the components, in meters, a 4.25, ay 1.97, b 1.72, by 5.04. (a) Find the angle between the directions of a and b There are two vectors in the xy plane that are perpendicular to a and have a magnitude of 8.86 m. One, vector c has a positive x component and the other, vector d a negative x component. What are (b) the x component and (c) the y component of c and (d) he x component and (e) the y component of vector d (a) Number Units Units (b) Number (c) Number Units (d) Number Units (e) Number

Explanation / Answer

ax=4.25,ay=1.97,bx=1.72, by=5.04

a) angle can be calculated as

arctan(5.04 / 1.72) - arctan(1.97 / 4.25)

= 71.04-24.6

=46.44 degrees

b)First we will find some intermediate numbers.
A=Sqrt(4.25^2 + 1.97^2) = 4.68
8.86 / 4.68 = 1.89 = q (scaling factor)
x component of c = 1.97 * q

=1.97*1.89

= 3.72m --answer to b

c)y component of c = -4.25 * q

=-4.25*1.89

= -8.03m

d)x component of d = -ay * q

=-1.97*1.89

= -3.72m

e)y component of d = ax * q

=4.25*1.89

= 8.03m

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