basis vectors?

Question

how do i work out what x and y are from this equation:

xa + yb = 7i + 6j - 11k

where a = 4i + 6j - 2k
and b = 2i - 6k

Answer 1

xa + yb = 7i + 6j - 11k
a = 4i + 6j - 2k
b = 2i - 6k
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x(4i + 6j - 2k) + y(2i - 6k) = 7i + 6j - 11k
4xi + 6xj – 2xk +2yi -6yk = 7i + 6j - 11k
(4x + 2y -7)i + (6x - 6)j + (–2x -6y +11)k = 0
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4x + 2y -7 = 0
6x – 6 = 0
–2x -6y +11 = 0
-
x = 1
y = 1.5
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