Mathematics Part-II

Book: Mathematics Part-II

Chapter: 10. Vector Algebra

Subject: Maths - Class 12th

Q. No. 14 of Exercise 10.2

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14

Show that the vector is equally inclined to the axes OX, OY and OZ.

To find the inclination of the vector with OX, OY, OZ. We find the direction cosines of the vector.


We know that the direction cosines of a vector are defined as the coefficients of in the unit vector in the direction of the vector.


So, first we find the unit vector in the direction of the vector.


Let




Therefore, The direction cosines of the given vector are .


Let be the angle between and OX.


Therefore,



Similarly, Let be the angle between and OY.


Therefore,



And, be the angle between and OZ.


Therefore,



Therefore,


Hence proved that the vector is equally inclined with the axes OX, OY, and OZ.


14

Chapter Exercises

Exercise 10.1
Exercise 10.2
Exercise 10.3
Exercise 10.4
Miscellaneous Exercise

More Exercise Questions

1

Compute the magnitude of the following vectors:
2

Write two different vectors having same magnitude.
3

Write two different vectors having same direction.
4

Find the values of x and y so that the vectors are equal.
5

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).
6

Find the sum of the vectors

7

Find the unit vector in the direction of the vector

8

Find the unit vector in the direction of vector where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.
9

For given vectors, find the unit vector in the direction of the vector

10

Find a vector in the direction of vector which has magnitude 8 units.
11

Show that the vectors are collinear.
12

Find the direction cosines of the vector

13

Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.
14

Show that the vector is equally inclined to the axes OX, OY and OZ.
15

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are respectively, in the ratio 2 : 1

(i) internally (ii) externally
16

Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2).
17

Show that the points A, B and C with position vectors, respectively form the vertices of a right angled triangle.
18

In triangle ABC (Fig 10.18), which of the following is not true:


(a)


(b)


(c)


(d)

19

are two collinear vectors, then which of the following are incorrect:

(a)


(b)


(c) the respective components of are not proportional


(d) both the vectors have same direction, but different magnitudes.