Three Dimensional Geometry questions
879 published questions with worked solutions.
- A point on a line has coordinates (p+1, p-3, 2 p) where p is any real number. What are the direction cosines of the line?
- A point on the line x-1 1 = y-3 2 = z+2 7 has coordinates
- If the line x-4 1 = y-2 1 = z-k 2 lies on the plane 2x-4y+z=7, then what is the value of k?
- A straight line passes through the point (1, 1, 1) makes an angle 60^ with the positive direction of z-axis, and the cosine of...
- If the points (x, y, -3), (2, 0, -1) and (4, 2, 3) lie on a straight line, then what are the values of x and y respectively?
- Let ABC be a triangle. If D(2, 5) and E(5, 9) are the mid-points of the sides AB and AC respectively, then what is the length of...
- If a line has direction ratios <a+b, b+c, c+a>, then what is the sum of the squares of its direction cosines?
- Into how many compartments do the coordinate planes divide the space?
- What is the equation of the plane which cuts an intercept 5 units on the z-axis and is parallel to xy-plane?
- Let A be a point in space such that | OA |=12, where O is the origin. If OA is inclined at angles 45^ and 60^ with x-axis and...
- If the point (x, y) is equidistant from the points (2a, 0) and (0, 3a) where a>0, then which one of the following is correct?
- If a , b , c are the position vectors of the vertices A, B, C respectively of a triangle ABC and G is the centroid of the...
- Consider the points A(2, 4, 6), B(-2, -4, -2), C(4, 6, 4) and D(8, 14, 12). Which of the following statements is/are correct? 1....
- A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?
- Consider the following statements : 1. The direction ratios of y-axis can be <0, 4, 0> 2. The direction ratios of a line...
- If L is the line with direction ratios 3, -2, 6 and passing through (1, -1, 1), then what are the coordinates of the points on L...
- Which one of the planes is parallel to the line x-2 3 = y-3 4 = z-4 5 ?
- If <l, m, n> are the direction cosines of a normal to the plane 2x-3y+6z+4=0, then what is the value of 49(7l^2+m^2-n^2)?
- A line through (1, -1, 2) with direction ratios <3, 2, 2> meets the plane x+2y+3z=18. What is the point of intersection of line...
- If p is the perpendicular distance from origin to the plane passing through (1, 0, 0), (0, 1, 0) and (0, 0, 1), then what is 3p^2...
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