The figure shows three points A B and C Determine the follow

The figure shows three points, A, B, and C. Determine the following position vectors in meters. (Express your answers in vector form.) Determine the following unit vectors. (Express your answers in vector form.)

Solution

d)

r A/B = rA - rB = -5 i + j + 8k

e)

rB/C = rB - rC

= 9 i + 6j - 3k

f)

uA = (1i + 4j +7k)/sqrt(1^2+4^2+7^2)

= 1/sqrt(66) i + 2/sqrt(66) j + 7/sqrt(66) k

g)

uB = (6i+3j-k)/sqrt(6^2+3^2+1^2)

= 6/sqrt(46) i + 3/sqrt(46) j - 1/sqrt(46) k

h)

uAC = (4i + 7j + 5k)/sqrt(4^2+7^2+5^2)

= 4/sqrt(90) i + 7/sqrt(90) j + 5/sqrt(90) k

i)

uC/B = (-9i -6j+3k)/sqrt(9^2+6^2+3^2)

= -9/sqrt(126) i - 6/sqrt(126) j + 3/sqrt(126) k