# 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) (b)

(c) (d) None of these

**(ii)** If then evaluate

(a) 0 (b) 4

(c) 3 (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) (b)

(c) (d)

**(v)** The area of parallelogram formed by and as

diagonals is

(a) 70 (b) 35

(c) (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) F**ind 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