We have to determine the projection of the force vector
P=10i-8j+14k lb on the line originating from (2,-5,3) and going towards the point
(5,2,-4)
The length of the line between (2,-5,3) and
(5,2,-4) is sqrt[ (5-2)^2+(2+5)^2+(-4-3)^2]
= sqrt
107.
The unit vector along the line joinging the two points
is:
(5-2)i /sqrt 107 + (2+5)j/sqrt 107 + (-4-3)k /sqrt
107
=> 3/ sqrt 107 i + 7 / sqrt 107 j - 7 / sqrt 107
k
=> 0.29 i + .67 j - .67
k
The projection of the the vector P=10i-8j+14k on the line
is the dot product between the two
=> (10i - 8j +
14k) * (0.29i + 0.67j - 0.67k)
=> 2.9 - 5.42 -
9.48
=>
-12
Therefore the dot product is equal to -12
Therefore the projection of P
on the required line is -12.
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