平面内给定三个向量a=(3,2),b=(-1,2),c=(4,1),(1)求满足a=mb+nc的实数m,n的值(2)若向量d=(x,y)满足d//(a+b),且/d/=5 ,求向量d
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![平面内给定三个向量a=(3,2),b=(-1,2),c=(4,1),(1)求满足a=mb+nc的实数m,n的值(2)若向量d=(x,y)满足d//(a+b),且/d/=5 ,求向量d](/uploads/image/z/3688074-18-4.jpg?t=%E5%B9%B3%E9%9D%A2%E5%86%85%E7%BB%99%E5%AE%9A%E4%B8%89%E4%B8%AA%E5%90%91%E9%87%8Fa%3D%283%2C2%29%2Cb%3D%28-1%2C2%EF%BC%89%2Cc%3D%284%2C1%29%2C%EF%BC%881%EF%BC%89%E6%B1%82%E6%BB%A1%E8%B6%B3a%3Dmb%2Bnc%E7%9A%84%E5%AE%9E%E6%95%B0m%2Cn%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%8B%A5%E5%90%91%E9%87%8Fd%3D%EF%BC%88x%2Cy%29%E6%BB%A1%E8%B6%B3d%2F%2F%EF%BC%88a%2Bb%29%2C%E4%B8%94%2Fd%2F%3D5+%2C%E6%B1%82%E5%90%91%E9%87%8Fd)
平面内给定三个向量a=(3,2),b=(-1,2),c=(4,1),(1)求满足a=mb+nc的实数m,n的值(2)若向量d=(x,y)满足d//(a+b),且/d/=5 ,求向量d
平面内给定三个向量a=(3,2),b=(-1,2),c=(4,1),(1)求满足a=mb+nc的实数m,n的值
(2)若向量d=(x,y)满足d//(a+b),且/d/=5 ,求向量d
平面内给定三个向量a=(3,2),b=(-1,2),c=(4,1),(1)求满足a=mb+nc的实数m,n的值(2)若向量d=(x,y)满足d//(a+b),且/d/=5 ,求向量d
(1) a = mb + nc (3, 2) = m(-1, 2) + n(4,1) (3, 2) = (-m + 4n, 2m + n) ∴ -m + 4n = 3, 2m + n = 2 联立方程得 m = 5/9, n = 8/9 (2) a + kc = (3, 2) + k(4, 1) = (3 + 4k, 2 + k) 2b - a = 2(-1, 2) - (3, 2) = (-5, 2) ∵ (a + kc) // (2b - a) ∴ 2(3 + 4k) - (-5)(2 + k) = 0 解得 k = -16/13 (3) d - c = (x, y) - (4, 1) = (x - 4, y - 1) a + b = (3, 2) + (-1, 2) = (2, 4) ∵ (d - c) // (a + b) ∴ 4(x - 4) - 2(y - 1) = 0 2x - y - 7 = 0 ~ (1) 且∣d - c∣ = 1 ∴√ [(x - 4)² + (y - 1)² ] = 1 两边平方, (x - 4)² + (y - 1)² = 1 ~ (2) 联立(1), (2)式, 得 x = 4±√ 5/5 y = 1±2√5/5 解得 d = (4+√ 5/5, 1+2√ 5/5) 或 (4-√ 5/5, 1-2√ 5/5)
(1)-1m+4n=3,2m+n=2解得m=1,n=1(2)a+b=(2,4)因为平行,可设d=(2x.4x),(2x)^2+(4x)^2=5^2,x=√5/2,d=(√5,2√5)