Let a and b be three-dimensional vectors. Then \((5a + 7 b) \times (-a+ 3 b) = ka \times b\) for some scalar k. Find k.
The cross-product of a vector with itself is zero, so the LHS reduces to: 15(a x b) - 7(b x a) = 15(a x b) + 7(a x b) = 22(a x b)
So k = 22
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