## Chapter 24 – Scalar Or Dot Product Exercise Ex. 24.1

## Chapter 24 – Scalar Or Dot Product Exercise Ex. 24.2

Prove that: If the diagonals of a quadrilateral bisect

each other at right angles, then it is a rhombus.

(Pythagoras’s Theorem) Prove by vector method that in a

right angled triangle, the square of the hypotenuse is equal to the sum of

the squares of the other rum sides.

Prove by vector method that the sum of the squares of

the diagonals of a parallelogram is equal to the sum of the squares of its

sides.

Prove using vectors: The quadrilateral obtained by

joining mid-points of adjacent sides of a rectangle is a rhombus.

Prove that the diagonals of a rhombus are perpendicular

bisectors of each other.

Prove that the diagonals of a rectangle are

perpendicular if and only if the rectangle is a square.

If AD is the median of

D ABC, using vectors, prove that

AB^{2} + AC^{2}

= 2 (AD^{2} + CD^{2}).

If the median to the base of a triangle is

perpendicular to the base, then triangle is isosceles.

In a quadrilateral ABCD, prove that AB^{2} + BC^{2}

+ CD^{2}+ DA^{2} = AC^{2} + BD^{2}

+ 4 PQ^{2}, where P and Q are

middle points of diagonals AC and BD.

## Chapter 24 – Scalar Or Dot Product Exercise Ex. 24VSAQ

## Chapter 24 – Scalar Or Dot Product Exercise MCQ

Correct option: (c)

Correct option: (b)

Correct option: (d)

Correct option: (c)

(a) Null vector

(b) Unit vector

(c) Constant vector

(d) None of these

Correct option: (b)

Correct option: (c)

Correct option: (a)

- A circle
- An ellipse
- A hyperbola
- None of these

Correct option: (b)

Correct option: (b)

Correct option: (c)

Correct option: (d)

Correct option: (b)

Correct option: (b)

Correct option: (c)

Correct option: (c)

- 1
- 0
- 2
- -1
- -2

Correct option: (a)

Correct option: (b)

- Positive
- Negative
- 0
- None of these

Correct option: (c)

Correct option: (a)

Correct option: (c)

- (-4,7)
- [-4,7]
- R – [-4,7]
- R – (4,7)

Correct option: (c)

NOTE: Answer not matching with back answer.

Correct option: (d)

NOTE: Answer not matching with back answer.

Correct option: (d)

Correct option: (b)

Correct option: (d)

Correct option: (d)