Question

(a) In unit vector notation, what is r = a - b + c if: a=5i+4j-6k, b = -2i + 2j+3k, & c = 4i+3j+2k?

(b) Calculate the angle between r and the positive z-axis

(c) What is the component of a along the direction of b?

(d) What is the component of a perpendicular to the direction of b but in the plane of a and b?

I did a b and c. However, for question C I don't know why I had to use Ax= Acos(theta) and not Ay= Asin(theta).(like I found the angle which was 123, but I don't understand why did I had to plug it in in the Ax and not Ay please an explanation for this)

And for question D I have no clue, I just know that the cross product of vector a and b will give me a new vector perpendicular to a and b but i don't know what to do wit it.

Answer 1

(a)

Given data ....

vector r = a -b +c

              = 5i+4j-6k -( -2i + 2j+3k) + 4i+3j+2k

              = 11 i + 5 j + -7 k

(b)

the angle between r and the positive z-axis be θ then   r cos θ = -7

where  

r =magnitude of

r = √[11^ 2 + 5 ^ 2 +-7^ 2

= 13.964

SO,

cos θ = -7 / 13.964

               θ=120 degrees  

(c)

In this the direction of......

componen in direction of b = r B

where

B = unit vector in direction of vector b

= b / mod b

   the component of a along the direction of bis = r ( b / mod b )