MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>EXERCISE>Q 6

MEDIUM

12th CBSE

IMPORTANT

Earn 100

Prove that the diagonals of a rhombus are perpendicular bisectors of each other.

Important Questions on Scalar or Dot Product

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>EXERCISE>Q 7

Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>EXERCISE>Q 8

If

A D

is the median of

∆ A B C

, using vectors, prove that

A C

.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>EXERCISE>Q 9

If the median to the base of a triangle is perpendicular to the base, then triangle is isosceles.

HARD

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>EXERCISE>Q 10

In a quadrilateral

A B C D

, prove that

A B^{2} + B C^{2} + C D^{2} + D A^{2} = A C^{2} + B D^{2} + 4 P Q^{2}

where

P

and

Q

are middle points of diagonals

A C

and

B D

.

HARD

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 1

What is the value of

k

, if angle between vectors

\vec{a} a n d \vec{b}

with magnitudes

2

and

\sqrt{3}

respectively is

\frac{π}{k}

? Given

\vec{a} \cdot \vec{b} = \sqrt{3}

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 2

If

\vec{a}

and

\vec{b}

are two vectors such that

\vec{a} \cdot \vec{b} = 6, | \vec{a} | = 3

and

| \vec{b} | = 4 .

Write the projection of

\vec{a}

on

\vec{b}

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 3

Find the value of

x + y

, if the cosine of the angle between the vectors

4 \hat{i} - 3 \hat{j} + 3 \hat{k}

and

2 \hat{i} - \hat{j} - \hat{k}

is

\cos θ = \frac{x}{\sqrt{y}}

.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-2>Chapter 5 - Scalar or Dot Product>VERY SHORT ANSWER QUESTIONS (VSAQs)>Q 4

If the vectors

3 \hat{i} + m \hat{j} + \hat{k} and 2 \hat{i} - \hat{j} - 8 \hat{k}

are orthogonal , Find

m

.