在曲线x=t，y=-t2，z=t3的所有切线中，与平面x+2y+z=4平行的切线（）。
A．只有1条
B．只有2条
C．至少有3条
D．不存在
参考答案：B
解析：
求曲线上的点，使该点处的切向量τ与平面x+2y+z=4的法向量n=(1，2，1)垂直。曲线在切点处的切向量τ=(x'(t)，y'(t)，z'(t))=(1，-2t，3t2)
即1-4t+3t2=0，
解得t=1，
。(对应于曲线上的点均不在给定的平面上)
因此，只有两条这种切线。
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