Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

The document Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
All you need of JEE at this link: JEE

Addition of Vectors

Let a and b be any two vectors. From the terminal point of a, vector b is drawn. Then, the vector from the initial point O of a to the terminal point B of b is called the sum of vectors a and b and is denoted by a + b. This is called the triangle law of addition of vectors.

Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

Parallelogram Law

Let a and b be any two vectors. From the initial point of a, vector b is drawn and parallelogram OACB is completed with OA and OB as adjacent sides. The vector OC is defined as the sum of a and b. This is called the parallelogram law of addition of vectors.

The sum of two vectors is also called their resultant and the process of addition as composition.

Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

Properties of Vector Addition

(i) a + b = b + a (commutativity)

(ii) a + (b + c)= (a + b)+ c (associativity)

(iii) a+ O = a (additive identity)

(iv) a + (— a) = 0 (additive inverse)

(v) (k1 + k2) a = k1 a + k2a (multiplication by scalars)

(vi) k(a + b) = k a + k b (multiplication by scalars)

(vii) |a+ b| ≤ |a| + |b| and |a – b| ≥ |a| – |b|

Difference (Subtraction) of Vectors

If a and b be any two vectors, then their difference a – b is defined as a + (- b).

Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

Multiplication of a Vector by a Scalar

Let a be a given vector and λ be a scalar. Then, the product of the vector a by the scalar λ is λ a and is called the multiplication of vector by the scalar.

Important Properties

(i) |λ a| = |λ| |a|

(ii) λ O = O

(iii) m (-a) = – ma = – (m a)

(iv) (-m) (-a) = m a

(v) m (n a) = mn a = n(m a)

(vi) (m + n)a = m a+ n a

(vii) m (a+b) = m a + m b

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

pdf

,

shortcuts and tricks

,

Free

,

Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

,

Important questions

,

Objective type Questions

,

Extra Questions

,

Previous Year Questions with Solutions

,

Exam

,

past year papers

,

mock tests for examination

,

Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

,

ppt

,

Summary

,

video lectures

,

Sample Paper

,

MCQs

,

practice quizzes

,

Semester Notes

,

Addition and Multiplication of a Vector by a Scalar JEE Notes | EduRev

,

Viva Questions

,

study material

;