一道简单的向量题
已知A(-3,0),B(0,√3),O为坐标原点,点C在第二象限,且∠AOC=60°,向量OC=λ向量OA+向量OB,则实数λ的值是多少?需要解题过程...
已知A(-3,0),B(0,√3),O为坐标原点,点C在第二象限,且∠AOC=60°,向量OC=λ向量OA+向量OB,则实数λ的值是多少?
需要解题过程 展开
需要解题过程 展开
2个回答
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OC = λOA + OB
= λ(-3,0) + (0,√3)
= (-3λ,√3)
OA . OC = (-3,0). (-3λ,√3)
= 9λ ----(1)
also
OA . OC = |OA||OC| cos∠AOC
= 3. [√(9λ^2 + 3 )] .1/2 --(2)
(1)=(2)
6λ = √(9λ^2 + 3 )
36λ^2 = 9λ^2 + 3
λ^2 = 1/9
λ = 1/3 or -1/3 (rejected)
As C is 第二象限, => λ = 1/3
= λ(-3,0) + (0,√3)
= (-3λ,√3)
OA . OC = (-3,0). (-3λ,√3)
= 9λ ----(1)
also
OA . OC = |OA||OC| cos∠AOC
= 3. [√(9λ^2 + 3 )] .1/2 --(2)
(1)=(2)
6λ = √(9λ^2 + 3 )
36λ^2 = 9λ^2 + 3
λ^2 = 1/9
λ = 1/3 or -1/3 (rejected)
As C is 第二象限, => λ = 1/3
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