作业帮|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]B[π/3,π][π/3,π2/3]D[π/6,π]
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/17 21:46:33
![|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]B[π/3,π][π/3,π2/3]D[π/6,π]](/uploads/image/z/11514831-15-1.jpg?t=%7C%E5%90%91%E9%87%8Fa%7C%3D3%7C%E5%90%91%E9%87%8Fb%7C%E2%89%A00%2C2x%26%23178%3B%EF%BC%8B2%7C%E5%90%91%E9%87%8Fa%7Cx%EF%BC%8B3%E5%90%91%E9%87%8Fa%E5%90%91%E9%87%8Fb%3D0%E6%9C%89%E5%AE%9E%E6%A0%B9%2C%E5%88%99%E5%90%91%E9%87%8Fa%E5%90%91%E9%87%8Fb%E7%9A%84%E5%A4%B9%E8%A7%92%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4A%5B0%2C%CF%80%2F6%5DB%5B%CF%80%2F3%2C%CF%80%5D%5B%CF%80%2F3%2C%CF%802%2F3%5DD%5B%CF%80%2F6%2C%CF%80%5D)
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|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]B[π/3,π][π/3,π2/3]D[π/6,π]
|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]
B[π/3,π][π/3,π2/3]D[π/6,π]
|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]B[π/3,π][π/3,π2/3]D[π/6,π]
2x²＋2|向量a|x＋3向量a向量b=0有实根
则判别式=(2|向量a|)²-4*2*3向量a.向量b≥0
∴ 4|a|²-24|a|*|b|*cosA≥0
代入3|b|=|a|
∴ 4|a|²-8|a|²cosA≥0
∴ cosA≤1/2
∵ A ∈[0,π]
∴ π/3≤A≤π
选B