Finding the value of the cross product of 2 vectors without knowing the value of the vectors?

Linda Peters 2022-09-27 Answered
Suppose v and w are two vectors parallel to the plane
x + 2 y + 3 z = 7.
Suppose furthermore that v is perpendicular to w ,
v = 3 ,   w = 4.
How would you go about answering this question? I always reach a dead end when I try to solve v and w that satisfy the given information, I just don't know how to go about it. I tried to draw the plane and two parallel vectors, then I know the length of the cross product would be 12. Then what do I do now? How could you solve this to find vectors v and w ?
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Answers (1)

ahem37
Answered 2022-09-28 Author has 15 answers
You have:
u × v = n ( 1 , 2 , 3 ) | u × v | = | n | 1 2 + 2 2 + 3 2 = | n | 14 = 12 n = ± 12 14 u × v = ± 12 14 ( 1 , 2 , 3 )
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