Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 5

HARD

11th Tamil Nadu Board

IMPORTANT

Earn 100

Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side whose length is half of the length of the third side.

Important Questions on Vector Algebra

HARD

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 6

Prove that the line segments joining the midpoints of the adjacent sides of a quadrilateral form a parallelogram.

HARD

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 7

If

= \frac{\vec{B C}}{2}

and

\vec{b}

represent a side and a diagonal of a parallelogram, find the other sides and the other diagonal.

HARD

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 8

If

\vec{P O} + \vec{O Q} = \vec{Q O} + \vec{O R}

, prove that the points

P, Q, R

are collinear.

HARD

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 9

If

D

is the midpoint of the side

B C

of a triangle

A B C

, prove that

\vec{A B} + \vec{A C} = 2 \vec{A D}

.

HARD

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 10

If

G

is the centroid of a triangle

A B C

, prove that

\vec{G A} + \vec{G B} + \vec{G C} = \vec{0}

.

HARD

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 11

Let

A, B

and

C

be the vertices of a triangle. Let

D, E

and

F

be the midpoints of the sides

B C, C A

and

A B

respectively. Show that

\vec{A D} + \vec{B E} + \vec{C F} = 0 .

HARD

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 12

If

A B C D

is a quadrilateral and

E

and

F

are the midpoints of

A C

and

B D

respectively, then prove that

\vec{A B} + \vec{A D} + \vec{C B} + \vec{C D} = 4 \vec{E F}

.

EASY

11th Tamil Nadu Board

IMPORTANT

Mathematics Standard 11 Vol II>Chapter 2 - Vector Algebra>EXERCISE>Q 2

Find the direction cosines of a vector whose direction ratios are

1, 2, 3

.