If A=5a_x +3a_y +2a_z B=-a_x+4a_y +6a_z C=8a_x +2a_y find the values of alpha and beta such that alpha A + beta B +C is parallel to the y-axis.

balafiavatv 2022-08-08 Answered
If A = 5 a x + 3 a y + 2 a z
B = a x + 4 a y + 6 a z
C = 8 a x + 2 a y
find the values of α and β such that α A + β B + C is parallel to the y-axis.
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Answers (1)

nedervdq3
Answered 2022-08-09 Author has 13 answers
α A + β B + C =< 5 α β + 8 , 3 α + 4 β + 2 , 2 α + 6 β >
for this vector to be parallel to y-axis
we must have:
5 α β + 8 = 0 (1)
2 α + 6 β = 0 (2)
(1)*6+(2)
32 α + 48 = 0
α = 48 / 32 = 1.5
use (2)
2 ( 1.5 ) + 6 β = 0
β = 3 / 6 = 0.5
so
α = 1.5 , β = 0.5
will make α A + β B + C =< 5 α β + 8 , 3 α + 4 β + 2 , 2 α + 6 β > parallel to y-axis.
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