Test: Three Dimensional Geometry- Assertion & Reason Type Questions - Commerce MCQ
6 Questions MCQ Test - Test: Three Dimensional Geometry- Assertion & Reason Type Questions
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): The length of the intercepts on the coordinate axes made by the plane 5x + 2y + z – 13 = 0 are 13/5 , 13/2 , 13 unit
Reason (R): Given: Equation of plane
5x + 2y + z - 13 = 0
⇒ 5x + 2y + z = 13
⇒ 
⇒ 
∴ Length of intercepts are 13/5 , 13/2 , 13 units
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): P is a point on the line segment joining the points (3, 2, –1) and (6, –4, –2). If x coordinate of P is 5, then its y coordinate is –2.
Reason (R): The two lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular, iff aa’ + bb’ + cc’ = 0.
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): If two lines are in the same plane i.e., they are coplanar, they will intersect each other if they are non-parallel. Hence the shortest distance between them is zero.
If the lines are parallel then the shortest distance between them will be the perpendicular distance between the lines i.e., the length of the perpendicular drawn from a point on one line onto the other line.
Reason (R): The angle between the lines with direction ratio 〈a1 ,b1, c1〉 and 〈a2 ,b2, c2〉 is given by:
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): The angle between the straight lines
Reason (R): Skew lines are lines in different planes which are parallel and intersecting.
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): Direction cosines of a line are the sines of the angles made by the line with the negative directions of the coordinate axes.
Reason (R): The acute angle between the lines x – 2 = 0 and 
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): x2 + y2 + z2 + 4x – 6y – 8z = 7 the equation to the sphere whose centre is at (–2, 3, 4) and radius is 6 units.
Reason (R): Given: Centre is at (–2, 3, 4) and r = 6
⇒ (x0, y0, z0) = (–2, 3, 4) and r = 6
We know that general equation of sphere is (x – x0)2 + (y – y0)2 + (z – z0)2 = r2
⇒ (x – (–2))2 + (y – 3)2 + (z – 4)2 = 62
⇒ (x + 2)2 + (y – 3)2 + (z – 4)2 = 62
⇒ x2 + 4x + 4 + y2 – 6y + 9 + z2 – 8z + 16 = 36
⇒ x2 + y2 + z2 + 4x – 6y – 8z + 29 = 36
⇒ x2 + y2 + z. + 4x – 6y – 8z = 7
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