- What are (a) the x component, (b) the y component, and (c) the z component of r = a - b +c if a= 7.8 + 6.6 - 7.1 , b= -2.9 + 7.4 + 3.9 , and c = 7.6 + 8.8 + 2.2 . (d) Calculate the angle between r and the positive z axis. (e) What is the component of along the direction of b? (f) What is the magnitude of the component of a perpendicular to the direction of b but in the plane of a and b?

Explanation:

a= 7.8i + 6.6j - 7.1k

b=   -2.9 i+ 7.4 j+ 3.9k , and

c = 7.6i + 8.8j + 2.2k

r = a - b +c

=7.8i + 6.6j - 7.1k - ( -2.9i + 7.4j+ 3.9k )+ ( 7.6i + 8.8j + 2.2k)

= 7.8i + 6.6j - 7.1k +2.9i - 7.4j- 3.9k )+  7.6i + 8.8j + 2.2k

= 18.3 i +18.3 j - k

the angle between r and the positive z axis.

cosθ = 18.3 / √18.3² +18.3² +1

the angle between r and the positive z axis.

= 18.3 / 25.75

cos θ= .71

45 degree

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explanation: