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

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 positivez-axis (c) What is the component of a along the direction of b? (d) What is the component of a perpendicular to the directionof b but in the plane of a and b? I am completely lost. I have no clue how to find r.. I willaward lifesaver to good answer.
(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 positivez-axis (c) What is the component of a along the direction of b? (d) What is the component of a perpendicular to the directionof b but in the plane of a and b? I am completely lost. I have no clue how to find r.. I willaward lifesaver to good answer.

Explanation / Answer

a - b + c = (5+2+4)i + (4-2+3)j + (-6-3+2)k = r r = 11i +5j -7k      (i,j,k) are theunit vectors length of r is (112 +52 + 72) = 13.96   call thisR r dot k = R k cos = R cos -7 = 13.96 cos     cos =-7/13.96   = 120 deg   angle between rand k (z-axis) A = 8.77 B = 4.12    lengths of A andB (same way we found length R) a dot b = A B cos    find the angle the sameway that as above then A cos will give you the component of a inthe b direction For the last part: b cross any vector is perpendicular to b (using thevector cross product) a dot that cross product would be the component of the vectorin the plane of a & b since b dot that vector would be zero (not sure what they areasking here since there are any number of vectors perpendicular to b)

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