(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 have calculated r = 11i+5j-7k. I am not certain what to doafter this. Please help with steps? (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 have calculated r = 11i+5j-7k. I am not certain what to doafter this. Please help with steps?

Explanation / Answer

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). component 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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