Maths · Direction ratios and direction cosines and the angle between two intersecting lines
The plane and the line are related as
The plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}-\boldsymbol{6}=\mathbf{0} \) and the line \( \frac{x}{1}=\frac{y}{2}=\frac{z}{3} \) are related as
- A. Parallel to the plane
- B. At right angle to the plane
- C. Lies in the plane
- D. Meets the plane obliquely
Step-by-step solution
The direction ratios of the line are (1,2,3) and the normal vector of the plane is (1,-2,1). Their dot product is 1*1 + 2*(-2) + 3*1 = 0, so the line is perpendicular to the normal, hence parallel to the plane. Since the point (0,0,0) on the line does not satisfy the plane equation (0-0+0-6=-6≠0), the line is not in the plane.
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