Given the vector a = (− 3,4), the vector B is opposite to the direction of a, and B = λ a, | B | = 1, then the real number λ=______ ．

Given the vector a = (− 3,4), the vector B is opposite to the direction of a, and B = λ a, | B | = 1, then the real number λ=______ ．


∵ a = (− 3,4), | a | = 5, ∵ B is opposite to a, B = λ a, | B | = 1, | λ = − 15, so the answer is: − 15



For any two vectors a and B, if there is a real number pair (λ, U) which is not all 0, such that λ a + UB = 0, then a and B are collinear. How to prove?


∵ λ a + UB = 0 (vector)
∴λa=-ub
∵λ, u are not all zero
Let λ≠ 0
Then a = - U / λ * B
A, B are collinear

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