已知点a(-2,4),b(m,4),若向量ba与向量i=(1,0)的夹角的余弦值为-2倍根号5/5,则m等于多少?
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![已知点a(-2,4),b(m,4),若向量ba与向量i=(1,0)的夹角的余弦值为-2倍根号5/5,则m等于多少?](/uploads/image/z/11472743-47-3.jpg?t=%E5%B7%B2%E7%9F%A5%E7%82%B9a%EF%BC%88-2%2C4%EF%BC%89%2Cb%28m%2C4%29%2C%E8%8B%A5%E5%90%91%E9%87%8Fba%E4%B8%8E%E5%90%91%E9%87%8Fi%3D%EF%BC%881%2C0%29%E7%9A%84%E5%A4%B9%E8%A7%92%E7%9A%84%E4%BD%99%E5%BC%A6%E5%80%BC%E4%B8%BA-2%E5%80%8D%E6%A0%B9%E5%8F%B75%2F5%2C%E5%88%99m%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
已知点a(-2,4),b(m,4),若向量ba与向量i=(1,0)的夹角的余弦值为-2倍根号5/5,则m等于多少?
已知点a(-2,4),b(m,4),若向量ba与向量i=(1,0)的夹角的余弦值为-2倍根号5/5,则m等于多少?
已知点a(-2,4),b(m,4),若向量ba与向量i=(1,0)的夹角的余弦值为-2倍根号5/5,则m等于多少?
ba=m*(-2)+4*4=-2m+16.
ba.i=(-2m+16).(1,0)=(-2m+16)=-2m+16,
|ba|=√(-2m+16)^2=|-2m+16|=-(-2m+16)=2m-16 (2m+160)
|i |=√(1^2+0)^2=1.
cos=(-2m+16)/|ba||i|=-2√5/5.
=(-2m+16)/(2m-16)*1=-2√5/5.
-2m+16=(-2√5/5)*(2m-16).
=-2√5/5*2m+16*2√5/5.
2m[(2√5/5)-1]=16[(2√5/5)-1].
2m=16.
∴m=8.----j即为所求.
当 -m+16>0时,题目无解.