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How would i find these vectors? I have no idea!?
For u=(26,6,−21) and v=(−18,−6,12), find the vectors u1 and u2 such that:
(i) u1 is parallel to v
(ii) u2 is orthogonal to v
(iii) u = u1 + u2
1 Answer
- 1 decade agoFavorite Answer
Any vector that is scalar multiple of v would be parallel to v
ie. k( -18, -6, 12 ) is parallel to v where k is any real number.
u1 = (-18k, -6k, 12k)
u2 is orthogonal to v. Say let u2 be (a, b, c)
u2. v = 0
-18a-6b+12c = 0
-3a-b+2c=0
b=-3a+2c
since u = u1+u2
-18k+a = 26
-6k+b = 6
12k+c = -21
but b = -3a+2c
thus the 3 equations
-18k + a = 26
-6k -3a + 2c = 6
12k + c = -21
solving k = -1.5, a = -1 c = -3, b = -3
u1= (27, 9, -18)
u2= (-1,-3,-3)
