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cosθ = (a · b)/(|a| |b|)
= [(4)(- 1) + (3)(2)]/[√(4² + 3²) · √(1² + 2²)] = 2/(5√5)
θ = 79.695°
a - λb = (4i + 3j) - λ(- i + 2j) = (4 + λ)i + (3 - 2λ)j
2a + b = 2(4i + 3j) + (- i + 2j) = 7i + 8i
(a - λb) · (2a + b) = 0，因为垂直
[(4 + λ)i + (3 - 2λ)j] · (7i + 8i) = 0
(4 + λ)(7) + (3 - 2λ)(8) = 0
λ = 52/9
= [(4)(- 1) + (3)(2)]/[√(4² + 3²) · √(1² + 2²)] = 2/(5√5)
θ = 79.695°
a - λb = (4i + 3j) - λ(- i + 2j) = (4 + λ)i + (3 - 2λ)j
2a + b = 2(4i + 3j) + (- i + 2j) = 7i + 8i
(a - λb) · (2a + b) = 0，因为垂直
[(4 + λ)i + (3 - 2λ)j] · (7i + 8i) = 0
(4 + λ)(7) + (3 - 2λ)(8) = 0
λ = 52/9
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