(a) In unit vector notation, what is r = a - b + c if: a=5i+4j-6k, b = -2i + 2j+
ID: 1576623 • Letter: #
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.
Explanation / Answer
(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 then r cos = -7
where
r =magnitude of
r = [11^ 2 + 5 ^ 2 +-7^ 2
= 13.964
SO,
cos = -7 / 13.964
=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 )
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