Vectors, Spaces

Question 1

Linear combination of two vectors

Answer 1

X,Y = aX+bY
where a,b∈R, X,Y∈V (here V is set of vectors)

Question 2

Explain the multiplication of vector with scalar

Answer 2

If α∈R then αX = α[x₁ x₂ ….Xₙ]

Question 3

What is linear combination of one vector

Answer 3

Multiplication of vector with scalar
If α∈R then αX = α[x₁ x₂ ….Xₙ]

Question 4

What is the scalar multiple of vector

Answer 4

Linear combination of one vector
If α∈R then αX = α[x₁ x₂ ….Xₙ]

Question 5

Operations of vectors

Answer 5

Addition
Subtraction
Multiplication of vector with scalar
Products of vectors - 1.Dot Product 2.Cross Product

Question 6

How many vectors generate by linear combination of vectors

Answer 6

Infinite number of vectors(space)

Question 7

Type of product of vectors

Answer 7

Two type
1.)Dot Product
2.)Cross product

Question 8

Another name of dot product

Answer 8

Inner product

Question 9

Give me two another names of dot product

Answer 9

Inner product
Scalar product

Question 10

Dot product gives what

Answer 10

Scalar quantity

Question 11

Notation for dot product

Answer 11

Question 12

All three notations for dot product

Answer 12

Question 13

Give mathematical formula of dot product

Answer 13

<X,Y> = XᵀY

Question 14

Is <X,Y> = <Y,X>

Answer 14

Yes

Question 15

<X,Y> = <Y,X> it implies what

Answer 15

XᵀY = YᵀX

Question 16

If dot product is zero then

Answer 16

vectors are orthogonal vectors
i.e angle between vectors is 90degree

Question 17

If vectors are orthogonal then

Answer 17

their dot product is zero

Question 18

Norm of vector

Answer 18

Length of vector