Question

Diketahui vektor-vektor

Answer 1

U = 2i - j + 2k
v = 4i + 10j - 8k
u + cv tegak lurus pada u.
u + cv = (2,-1,2) + c(4,10,-8)
u + cv = (2,-1,2) + (4c,10c,-8c)
u + cv =(2+4c,-1+10c,2-8c)
syarat tegak lurus adalah
(u + cv).u = 0
(2+4c,-1+10c,2-8c).(2,-1,2) = 0
2(2+4c)+(-1)(-1+10c)+2(2-8c) = 0
4+8c+1-10c+4-16c = 0
9-18c = 0
-18c = -9
c=
c=

Answer 2

U = 2i - j + 2k  dan v = 4i + 10j - 8k
u + c.v  = (2 , -1 , 2 ) + (4c , 10c , -8c)
            = (2+ 4c , -1 + 10c , 2 - 8c)
cos α = (u. u +cv) / IuIIvI
cos 90 drjt = (u.v) / IuIIu +cvI
             0 =  (u.v) / IuIIu+cvI
             u. u +cv = 0
2(2+4c) + -1(-1 + 10c) + 2(2 - 8c) = 0
4 + 8c + 1 - 10c + 4 - 16c = 0
-18c + 9 = 0
 -18c = -9
     c = 1/2