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Thought-Process to Discover Knowledge

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nub,

trek,

jogger,

exercise.

User Guide

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summary of this topic

### Multiplication of Vectors by Scalar

Voice

Voice

Home

»  Repeated addition is generalized to Multiplication of a vector by Scalar

»  Components are multiplied by scalar
→  vec p = ai + bj + ck
→  lambda vec p = lambda a i + lambda b j + lambda c k

### Repeated addition of a Vector

plain and simple summary

nub

plain and simple summary

nub

dummy

When vector is multiplied by a scalar, the vector scales up or down proportionally.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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We have learned about addition of two or more vectors. Consider a vector being repeatedly added to itself. What is the result of the addition vec p + vec p?

• sum = 2 times vec p
• component form is required to find the sum
• directional cosines are required to find the sum
• sum =2 times |vec p|

The answer is 'sum = 2 times vec p'. If vec p = ai+bj+ck then vec p + vec p = 2ai+2bj+2ck. This equals 2 times vec p.

Repeated addition can be generalized to multiplication of vector by a scalar. Scalar multiplier is denoted with lambda to identify differently to the component values a, b, c. Note that the scalar multiplier and component values are real numbers. What is the result of lambda vec p if vec p = ai+bj+ck?

• lambda ai+bj+ck
• lambda i+ lambda j + lambda k
• lambda ai+ lambda bj + lambda ck
• lambda sqrt(a^2+b^2+c^2)

The answer is 'lambda a i+ lambda b j + lambda c k'.

Can a vector vec p be divided by a real number lambda?

• Yes. Division is inverse of multiplication.
• No. Division of vector is not defined.

The answer is 'Yes. Division is inverse of multiplication.'

If the given vector is vec p = ai+bj+ck then
vec p -: lambda
quad quad = 1/lambda xx vec p
quad quad = a/lambda i+b/lambda j+c/lambda k

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Multiplication of Vector by a scalar: For any vector vec p = ai + bj+ ck in bbb V and scalar lambda in RR
lambda vec p= lambda ai+ lambda bj + lambda ck`

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

We have learned about addition of two or more vectors. Consider a vector being repeatedly added to itself. What is the result of the addition vector p + vector p?
1
2
3
4
The answer is "sum = 2 times vector p". If vector p = a i + b j + c k ; then vector p plus vector p = 2 a i + 2 b j + 2 c k. This equals 2 times vector p.
Repeated addition can be generalized to multiplication of vector by a scalar. Scalar multiplier is denoted with lambda to identify differently to the component values a, b, c. Note that the scalar multiplier and component values are real numbers. What is the result of lambda times vector p ; if vector p = ai + b j + c k?
1
2
3
4
The answer is ' lambda a i+ lambda b j + lambda c k '.
When vector is multiplied by a scalar, the vector scales up or down proportionally.
Multiplication of Vector by a scalar: For any vector p = a i + b j+ c k in vector space V ; and scalar lambda in real numbers. lambda times vector p = lambda a i+ lambda b j + lambda c k
can a vector p be divided by a real number lambda?
yes;s;inverse;multiplication
Yes. Division is inverse of multiplication.
no;not;defined
No. Division of vector is not defined.
The answer is "Yes. Division is inverse of multiplication". If the given vector is vector p = a i + b j + c k ; then vector p divided by lambda ; equals 1 by lambda, multiplied by vector p.

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