Learn Vector Algebra with Free Lessons & Tips

Vector is that quantity that has direction and magnitude

for example force, velocity, acceleration and displacement

The scaler is that quantity which has the only magnitude

for example speed, volume, mass temperature, power, energy and time

The measure of a vector is a scalar quantity.

A scalar can multiply vectors. The result is another vector.

Suppose c is a scalar and v = (a, b) is a vector, then the scalar multiplication would be cv = c (a, b) = (ca, cb). Hence each component of vector gets multiplied by the scalar.

If two vectors are of the same dimension, they can be added or subtracted from each other. The result is gain a vector.

Some Basic Rules of Algebra of Vectors:

a.a = |a|2 = a2

a.b = b.a

a.0 = 0

a.b = (a cos q)b = (projection of a on b)b = (projection of b on a) a

a.(b + c) = a.b + a.c (This is also termed as the distributive law)

(la).(mb) = lm (a.b)

(a ± b)2 = (a ± b) . (a ± b) = a2 + b2 ± 2a.b If a and b are non-zero, then the angle between them is given by cos θ = a.b/|a||b|

a x a = 0

a x b = - (b x a)

a x (b + c) = a x b + a x c

If two unit vector in same direction (along),third unit vector in opposite direction situated after applying law's of vector addition along coordinate we will gate unit vector..which is result of three unit vector.NOw in second case if two unit vector is 120 degree to each other the results will be equal to unit vector after applying law's of vector addition...if u split in cordcoordi system hardly matter,no result will change...