能力提升

1已知A(3,4,5),B(0,2,1),O(0,0,0),若(OC) ⃗=2/5 (AB) ⃗,则点C的坐标是(　　)

A.("-" 6/5 ",-" 4/5 ",-" 8/5) B.(6/5 ",-" 4/5 ",-" 8/5)

C.("-" 6/5 ",-" 4/5 "," 8/5) D.(6/5 "," 4/5 "," 8/5)

解析:∵(AB) ⃗=(-3,-2,-4),

　　∴2/5 (AB) ⃗=("-" 6/5 ",-" 4/5 ",-" 8/5).

　　设点C的坐标为(x,y, ),

　　则(OC) ⃗=(x,y, )=2/5 (AB) ⃗=("-" 6/5 ",-" 4/5 ",-" 8/5).故选A.

答案:A

2已知a=(1,0,1),b=(-2,-1,1),c=(3,1,0),则|a-b+2c|等于(　　)

A.3√10 B.2√10 C.√10 D.5

解析:∵a-b+2c=(3,1,0)+(6,2,0)=(9,3,0),

　　∴|a-b+2c|=√90=3√10.

答案:A

3已知a=(1-t,1-t,t),b=(2,t,t),则|b-a|的最小值是(　　)

A.√5/5 B.√55/5 C.(3√5)/5 D.11/5

解析:∵b-a=(1+t,2t-1,0),

　　∴|b-a|2=(1+t)2+(2t-1)2+02=5t2-2t+2

　　=5(t"-" 1/5)^2+9/5.

　　∴|b-a"|" _min^2=9/5.∴|b-a|min=(3√5)/5.

答案:C

4已知A(1,-2,11),B(4,2,3),C(6,-1,4),则△ABC的面积是(　　)

A.(5√42)/2 B.5√42

C.5√3 D.5√14

解析:∵(AC) ⃗=(5,1,-7),(BC) ⃗=(2,-3,1),