# Case study Chapter 10 (Vectors)

Solar panels have to be installed carefully so that the tilt of the roof, and the direction to the sun , produce the largest possible electrical power in the solar panals.(Case study problem vector 1)

A surveyor uses his instrument to determine the co-ordinates of the four corners of a roof where solar panels are to

be mounted. In the picture, suppose the points are labelled counter clockwise from the roof corner nearest to the

camera in units of meters and .

Based on the above information answer the following question.

(i) Find the components to the two edge vectors defined by and ?

(ii) (a) Find the magnitudes of the vectors and .

(b) Find the components to the vectors , perpendicular to and and the surface of the roof.

Solution: Given points are and .

(i) We have,

Components of vector A are

and

Components of vector B are .

(ii) (a) We have

units

units

(b) We have,

Its components are

2. Read the following and answer the question:

A class XII student appearing for a competitive examination was asked to attempt the following question.

Let and be three non zero vectors.

(i) If and are such that

(a) Â  Â  Â  Â  Â  Â  Â  Â  Â (b)

(c) Â  Â (d) None of these

(ii) If then evaluate

(a) 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 4

(c) 3Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 2

(iii) If and are unit vectors and be the angle between them then is

(a) (b)

(c) (d)

(iv) Let and be unit vectors such that and angle

between and is then

(a) Â  Â  Â  Â  Â  Â  Â (b)

(c) Â  Â  Â (d)

(v) The area of parallelogram formed by and as

diagonals is

(a) 70Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 35

(c) Â  Â  Â  Â (d)

Solution:(i) Answer (a)

Given,

(ii) Answer (a)

And

(iii) Answer(b)

Given,

(iv) Answer (c)

We have

And

Since angle between and is

(v) Answer (c)

The area of the parallelogram formed by and as diagonal

Now,

Area sq.units.

## Some other case study question

Case study: A man is watching an aeroplane which is at the co-ordinate point A(4, -1, 3) assuming that the man is at O(0, 0, 0). At the same time he saw a bird at the coordinate point B(2, 0, 4).

Based on the above information answer the following:

(a) Find the position vector

(b) Find the distance between aeroplane and bird

(c) Find the unit vector along .

(d) Find the direction cosine of .

(e) Find the angles which makes with x, y and z axes.

Solution: For solution click here