Orthogonal projections to help find distance between 2 vectors..

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RM5152

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Hello all,
I have been asked to compute the distance from y to the straight line L that runs through u and the origin and I thought the best way was to find the orthogonal projection of vector y onto the Line L and then to find the distance between the 2 points (the orthogonal projection of y onto L and y) by using Pythagoras theorem for xyz space but my answer of 10.332 is coming up as wrong.. could anyone tell me where I am going wrong please? Thanks :)
 

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Please state the exact problem in its exact wording. Please do not post an image.
Give us the two vectors and the line.
 
pka said:
Please state the exact problem in its exact wording. Please do not post an image.
Give us the two vectors and the line
Click to expand...
okay the exact wording is: Let y = (-7,-3,-7) and u = (-6,4,7). Compute the distance d from y to the straight line through u and the origin. Thanks in advance for any help.
 
RM5152 said:
okay the exact wording is: Let y = (-7,-3,-7) and u = (-6,4,7). Compute the distance d from y to the straight line through u and the origin. Thanks in advance for any help.
Click to expand...
Which is it? y = (-7,-3,-7) or 1656341151643.png ?

Either you copied it wrong in your work, or you misstated the "exact wording"!
 
RM5152 said:
okay the exact wording is: Let y = (-7,-3,-7) and u = (-6,4,7). Compute the distance d from y to the straight line through u and the origin. Thanks in advance for any help.
Click to expand...
Thank you for the clarification. I [imath]\ell: P+t\overrightarrow D[/imath] is a line such that the point [imath]Q\notin \ell[/imath]
then the distance from [imath]Q[/imath] to [imath]\ell[/imath] is [imath]\mathbb{D}(Q,\ell)=\dfrac{\left\|\overrightarrow{PQ}\times\overrightarrow D\right\|}{\left\|\overrightarrow D\right\|}[/imath]
[math][/math][imath][/imath][imath][/imath][imath][/imath]
 
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