Class 11 - NCERT - Physics - Motion in a plane

types of vector addition

1) Triangle law 2) Polygon law 3) Parallelogram law They are commutative and associative.

If A= icos theta + jsin theta

A = sq root Ax^2 + Az^2

What is a unit vector?

A unit vector is a vector of unit length used to specify direction. It is dimensionless. They are just intended to specify direction.

What are vector quantities?

Any physical quantity which have both magnitude and direction . They follow laws of vector algebra . eg - momentum, velocity, impulse, angular momentum, torque, gravitational field, electric field, magnetic field

What are scalar quantities?

Physical quantities which have only magnitude which can either be negative or positive and a unit of measure. eg- mass, distance, average speed, temperature, instantaneous speed, energy, pressure density, charge

If theta = 180

R = a -b and R is minimum

if theta = 0

R is maximum

what are the types of vector products?

Scalar product or dot product Vector product or cross product

What are anti-parallel vectors?

When two vectors are in opposite direction, they are said to e anti-parallel.

projection - Vector component of a along b

a cos theta = a.b/b = a.b^

Area of a parallelogram

ab sin theta

Scalar product

abcos theta

Vector Product (non commutative and non associative) It is distributive

absin theta

tan alpha

b sin theta/a + bcos theta

tan alpha

b sin theta/a- bcos theta

for vector product

i . i = 0 i.j = k

for scalar product

i . i = 1 (here cos0) i.j = 0 (Here cos90)

AxBx + AyBy + AzBz

sq root (Ax^2 + Ay^2 + Az^2 ) x (Bx^2 + By^2 + Bz^2) cos theta

If theta = 180

sq root a^2 + b^2

Formula for resultant

sq root a^2 + b^2 + 2abcostheta

a - b

sq root a^2 + b^2 - 2abcostheta

Position vector r=

xi + yj + zk

What is a zero vector?

It is a vector with zero magnitude and undefined direction.

What is the angle between vectors?

It is the smaller angle between the tail's or head's of the two vectors.

What is equilibrium?

It means that net force acting on a body is zero.

What are parallel vectors?

If two vectors have same direction, they are parallel to each other.

What are equal vectors?

If two vectors have same magnitude and direction, they are parallel to each other.

What are negative vectors?

If two vectors have same magnitude and is in opposite direction.