The projection of the line segment joining (1,2,-1), (4,2,1) on the line x/2=-y=z is 7/2
True or false with correct explanation
1
Expert's answer
2020-11-17T16:41:00-0500
By definition, the projection of the line segment joining (1,2,−1),(4,2,1) on the line 2x=−1y=1z is a absolute value of the projection of the vector a=(4,2,1)−(1,2,−1)=(3,0,2) on the vector b=(2,−1,1) which is parallel to the above line. Therefore, prba=∣b∣∣a⋅b∣=4+1+1∣3⋅2+0⋅(−1)+2⋅1∣=68.
We conclude that it is not true that the projection of the line segment joining (1,2,−1),(4,2,1) on the line 2x=−1y=1z is 27.
Comments