NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 5
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Objective Type Questions
Choose the Correct Answer from the Given Four Options in Each of the Examples 14 to 19
Question 14:
The coordinates of the foot of the perpendicular drawn from the point on the axis are given by
(A)
(B)
(C)
(D)
Answer:
(A) is the correct answer.
Question 15:
P is a point on the line segment joining the points and . If co-ordinate of P is 5, then its y co-ordinate is
(A)
(B)
(C)
(D)
Answer:
(A) is the correct answer.
Let P divides the line segment in the ratio of coordinate of the point P may be expressed as giving so that
Question 16:
If are the angles that a line makes with the positive direction of axis, respectively, then the direction cosines of the line are.
(A)
(B)
(C)
(D)
Answer:
(B) is the correct answer.
Question 17:
The distance of a point from axis is
(A)
(B)
(C)
(D)
Answer:
(C) Is the correct answer. The required distance is the distance of from , which is .
Question 18:
The equations of axis in space are
(A)
(B)
(C)
(D)
Answer:
(D) Is the correct answer.
On axis the co-ordinate and co-ordinates are zero.
Question 19:
A line makes equal angles with co-ordinate axis. Direction cosines of this line are
(A)
(B)
(C)
(D)
Answer:
(B) is the correct answer. Let the line makes angle α with each of the axis. Then, its direction cosines are .
Since . Therefore,
Fill in the Blanks in Each of the Examples from 20 to 22
Question 20:
If a line makes angles with axis, respectively, then its direction cosines are _______
Answer:
The direction cosines are
Question 21:
If a line makes angles with the positive directions of the coordinate axes, then the value of is _______
Answer:
Note that
.