uestion 6 Determine the components of a unit vector that is perpendicular to bot

Question

uestion 6 Determine the components of a unit vector that is perpendicular to both OA and OB. Give the components of rOA i al (Nc decimal is needed) Give the components of rOAj b Give the components of rOAk c Give the components of rOB i Id (No decimal is needed) Give the components of rOB j e] Give the components of rOBk I For a UNIT vector that is perpendicular to the lines OA and OB give the components of e e component i is lel (Three decimals for the e components) e component jish e component k is Next give the length (magnitudej of the shortest straight line from point 6 to the straight line that passes through points O and A This distance is meters (Two decis (Hint Similar to the example 2.15 in the text book on page 73)

Explanation / Answer

OA = (9,-3,2)
hence
a) = 9
b) -3
c) 2
OB = ( 5,4,-2)
d) 5
e) 4
f) -2

unit vector perpendicular to OA * OB

= OA * OB / ||OA * OB||
OA * OB
= ((-3)·(-2) - 2·4) - j (9·(-2) - 2·5) + k (9·4 - (-3)·5) =
= {-2; 28; 51}

||OA * OB|| = sqrt( (-2)^2 + 28 ^2 + 51^2)
= 58.215118
e = {-2; 28; 51} /58.215118

g) -2/58.215118
h) 28/58.215118
i) 51/58.215118

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