Page 88 - Mathematics Class - XI

Case-Study Based Questions
Case-Study Based Questions

A three dimensional cartesian coordinate system is formed by a Z
point called the origin (represented by point O) and it consisting a
three mutually perpendicular vectors. These vectors define the three C N
coordinate axes like X, Y and Z axes. (x, y, z)
The coordinate of any point in the space is determined by three real L P
numbers x, y, z. The plane known as coordinate planes divides the space O Y B Y
into OCTANTS.
Figure, shown aside, depicts a rectangular parallelopiped based on A M
the above information answer the questions below. X

1. If point P represents the coordinate (3,6,5) then the coordinates of point N will be
(a) (3, 0, 5) (b) (0, 6, 5) (c) (3, 6, 0) (d) (0, 0, 0)

2. In which octant does the point (3, –2, –5) lies
(a) II (b) VI (c) VIII (d) IV
3. From the above fig., the coordinates of point B will be
(a) (0, 6, 0) (b) (0, 0, 5) (c) (0, 6, 5) (d) (3, 6, 0)

4. If a point lies on z-axis than the coordinates of the points are
(a) (x, y, z) (b) (x, y, 0) (c) (0, y, 0) (d) (0, 0, z)

Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 3: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.
Q. 1. Assertion (A) : The xy-plane divides the line joining the points (–1, 3, 4) and (2, –5, 6) externally in
the ratio 2:3.
Reason (R) : For a point in x–y plane, its z-coordinate should be zero.
Q. 2. Assertion (A) : Points (–4, 6, 10), (2, 4, 6) and (14, 0, –2) are collinear.
Reason (R) : Point (14, 0, –2) divides the line segment joining by other two given points in the
ratio 3 : 2 internally.
Q. 3. Assertion (A) : Points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.
Reason (R) : Three points A, B, and C are said to be collinear if AB + BC = AC

Answers

Case-Study Based Questions: 1. (b) 2. (c) 3. (a) 4. (d)

Assertion-Reason Based Questions: 1. (a) 2. (c) 3. (a)

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