Vectors and scaler

Raj Kumar
11/09/2018 0 0

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

0 Dislike
Follow 2

Please Enter a comment


Other Lessons for You

internal and external divison of vectors
If A and B are two points with position vectors a and b respectively and C is a point which divides AB internally in the ratio m: n, then the position vector of C is given by OC = (mb + na)/ (m + n). This...

Raj Kumar | 11/09/2018

0 0

Geometric Progression
If a is the first term and r is the common ratio of the geometric progression, then its nth term is given by an = arn-1 The sum Sn of the first n terms of the G.P. is given by Sn = a (rn – 1)/...

Raj Kumar | 06/09/2018

0 0

Notes on Arithmetic progression
If ‘a’ is the first term and ‘d’ is the common difference of the arithmetic progression, then its nth term is given by an = a+(n-1)d The sum, Sn of the first ‘n’...

Raj Kumar | 23/08/2018

0 0

Notes on Harmonic progression
Let a, b and c form an H.P. Then 1/a, 1/b and 1/c form an A.P. If a, b and c are in H.P. then 2/b = 1/a + 1/c, which can be simplified as b = 2ac/(a+c) If a and b are two non-zero numbers...

Raj Kumar | 23/08/2018

0 0

Cordinate Axis retangular to polar and polar to rectangular Conversion
The system of coordinates is known as the Cartesian System of Coordinates. It is so called because this system was first introduced by the philosopher Des Cartes. There are other systems of coordinates...

Raj Kumar | 20/08/2018

0 0

Looking to Learn?

Find best Tutors and Coaching Centers near you on UrbanPro.


Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you

Best Tutors and Trainers in your Locality Find Now » is India's largest network of most trusted tutors and institutes. Over 25 lakh students rely on, to fulfill their learning requirements across 1,000+ categories. Using, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 6.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more