Question

3icap+5jcap means according to vector algebra

Answer 1

Answer:

it Is 60°.

Solution: Do dot product.

let A= I+j nd B= 2j+2k

Now, A.B =|A||B|Cos(Theta)

        

(I+j).(2j+2k) = 4×Cos(Theta)

          2=4× Cos(Theta)

  

So Cos(Theta)= 1/2

    

So Theta=Angle = 60°

i tried to help you..... may you find it helpful.

Answer 2

QUESTION:

$Meaning\:\:of \:\: 3\hat i +5 \hat j \:\: according \: \: to\\vector \: \: algebra$

EXPLANATION:

• The meaning of $3\hat i +5 \hat j$ is that three units along x - axis and five units along y - axis .

• Here mentioned is in case of a 2-Dimension where only two co-ordinates are present.

• 2-Dimension is often mentioned as a plane.

• When $\hat k$ is present, it would be considersd as it possess 3 - Dimensions also.

• 3 - Dimension will have three co-ordinates that are x co-ordinate, y co-ordinate and z co-ordinate.

• 3 - Dimension is often referred to as space.

• Also $\hat i,\:\hat j,\:\hat k$ are referred to as unit vectors as their magnitude is one.

• Hence $\hat i$ is a unit vector along x direction(axis), when 3 is multiplied with that it indicates a vector having magnitude 3 units along x - direction.

• Similarly in the case of $5 \hat j$ which indicates 5 times of a unit vector along y - axis.

SOME FORMULAE RELATED TO VECTOR ALGEBRA:

CROSS PRODUCT = $\vec{A} \times \vec{B} = AB \sin \theta$

DOT PRODUCT = $\vec{A}.\vec{B} = AB \cos \theta$

SOME MORE POINTS:

CROSS PRODUCT:

• Cross product is also known as vector product as it always gives the resultant as a vector.

• $\vec{A} \times \vec{B} = - \vec{B} \times \vec{A}$

• Hence vector product is not commutative.

DOT PRODUCT :

• Dot product is also known as scalar product as it always gives the resultant as a scalar.

• $\vec{A} .\vec{B} = \vec{B} .\vec{A}$

• Hence scalar product is commutative.