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Vector Problem help needed?
Need help solving one or both
1 Answer
- ?Lv 76 years agoFavorite Answer
(a) AC = a+b; BD = b-a. (b) It's b^2 - a^2. (c) If |a| = |b| then b^2-a^2 = 0, and it is well known that two vectors whose dot product is zero are perpendicular to one another.
#2. (a) Dot product of the vectors is (4 + 1 + 16)*lambda. Their magnitudes are sqrt(21) and lambda*sqrt(21). Since their dot product is the product of their magnitudes, they are parallel; and furthermore both position vectors have the origin as their "rear" point; so OB coincides with OA.
(b) (12-2L, 2-L, 4-4L) "dot" (2,1,4) = 0 => 24-4L + 2 - L + 16 - 16L = 0 =>:42 = 21L => L = 2. (c) Now B is (4,2,8) and the distance is:
sqrt(8^2 + 0^2 + 4^2) = 4*sqrt(5).
