Engineering Board Exam Reviewer · Solid Analytic Geometry · easy

A line has direction numbers (2,-3,6). Find its direction cosine with respect to the z-axis.

1. 2/7
2. - 3/7
3. 6/7
4. 1/7

Answer

C. 6/7

Solution

The magnitude is sqrt(4+9+36)=7, so =6/7.

More Solid Analytic Geometry questions

1. Find the midpoint of the segment joining (2,-4,6) and (8,2,-2).
2. Find the distance between the points (1,2,3) and (4,6,15).
3. Find the volume of the tetrahedron with vertices (1,1,1), (3,1,1), (1,4,1) and (1,1,6).
4. Find the radius of the sphere with center (1,-2,3) that is tangent to the plane 2x-y+2z-3=0.
5. Find the point that divides the segment from (0,0,0) to (6,9,12) in the ratio 1:2 measured from the first point.
6. Find the angle between two lines with direction numbers (1,1,0) and (0,1,1), in degrees.
7. Find the distance between the parallel planes 2x-y+2z=4 and 2x-y+2z=13.
8. Find the distance from the point (2,-1,3) to the plane x+2y-2z+4=0.
9. Find the acute angle between the planes x+y+z=3 and x-y+z=5, in degrees.
10. Find the equation of the plane through (1,2,3) that is perpendicular to the vector (2,-1,4).

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