Vector Equation Line: lasers and targets

Is that really exactly how the problem is stated? It does not make much sense! "position vector q = (10, -10,20)in the direction given by v = (20,-30,10)". No, the "position vector" is NOT in the direction "given by v"! I can guess that you are referring to a line passing through the point given by position vector "v" with direction vector v, but then you ask about "t= 3". Where did "t" suddenly come from?

If the problem is "given a line passing through the point given by position vector q= (10, -10, 20) in the direction given by v= (20, -30, 10), parameterized by t such that the point (10, -10, 20) corresponds to t= 0 and (10+ 20, -10- 30, 20+ 10)= (30, -40, 30) corresponds to t= 1, what point corresponds to t= 3", then your answer is correct.
 
HallsofIvy said:
Is that really exactly how the problem is stated? It does not make much sense! "position vector q = (10, -10,20)in the direction given by v = (20,-30,10)". No, the "position vector" is NOT in the direction "given by v"! I can guess that you are referring to a line passing through the point given by position vector "v" with direction vector v, but then you ask about "t= 3". Where did "t" suddenly come from?

If the problem is "given a line passing through the point given by position vector q= (10, -10, 20) in the direction given by v= (20, -30, 10), parameterized by t such that the point (10, -10, 20) corresponds to t= 0 and (10+ 20, -10- 30, 20+ 10)= (30, -40, 30) corresponds to t= 1, what point corresponds to t= 3", then your answer is correct.
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I should have stated that and object was fired point given by the position vector q = (10, -10,20) in the direction given by v = (20,-30,10)
 
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