4 vectors a, b, c and d. a= 3i + 2j -6k d= 2i - j + k a is the sum of vectors b and c. Find b and c so that b is PARALLEL to d and c is PERPENDICULAR to d.
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Originally Posted by jenny 4 vectors a, b, c and d. a= 3i + 2j -6k d= 2i - j + k a is the sum of vectors b and c. Find b and c so that b is PARALLEL to d and c is PERPENDICULAR to d. Let vectors b and c be and Then Thus Now, b is parallel to d, so Thus Thus And finally c is perpendicular to d, so So we have the conditions: and and We have 7 variables in 7 unknowns. It'll take a while, but it should be solvable. -Dan
Originally Posted by jenny 4 vectors a, b, c and d. a= 3i + 2j -6k d= 2i - j + k a is the sum of vectors b and c. Find b and c so that b is PARALLEL to d and c is PERPENDICULAR to d. Vector is the orthogonal projection of on calculated by Then set Now check that and is parallel to since it is a multiple of it. Finally is perpendicular to since
Originally Posted by topsquark why should we automatically exclude the possibility that b might have a longer length than d? That method does not exclude the possibility that b might be longer than d. Moreover, the solution is unique.
Originally Posted by Plato That method does not exclude the possibility that b might be longer than d. Thanks for pointing that out. I wasn't looking at it right. :\ -Dan
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