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If a and b are not parallel, then for what value of α will the vectors u=(α-2)a+b and v=(2+3α)a-3b be collinear?

1. 3/2
2. 2/3
3. -3/2
4. -2/3

Correct answer: 2/3

Solution

For collinearity u=lambda*v: (alpha-2)=lambda(2+3alpha) and 1=-3lambda so lambda=-1/3. Substituting gives alpha-2=-(2+3alpha)/3, leading to 2alpha=4/3, alpha=2/3.

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