Question

Two vectors are given by 5 î - 3 Ĵ and 3 î - 5 ĵ. Calculate their scalar and vector products.​

Answer 1

Answer:

We are given, two vectors:

A =  5 î - 3 Ĵ  

B = 3 î - 5 ĵ.

The scalar product is ( 3 x 2 + ( 4 x -4 ) + 5 x 0 ) = - 10

A vector with component value 3 in x direction together with another of value 2 in the x direction will give a new vector of value 5

The scalar product of A and B = 5i + 5k

The vector product of A and B needs a specific calculation of cross multiplying the other values using one j and the other k and then subtracting the others.

A good way to see this is to form a table and multiply terms diagonally and downwards to the right and subtract in the opposite sense to the left.

Hope it helps u !!

Answer 2

Given:

2 vectors:

• 5î - 3ĵ
• 3î - 5ĵ

To find:

• Scalar product (dot product)
• Vector product (cross product)

Solution:

First let's find out the scalar product

(5î - 3ĵ). (3î - 5ĵ)

= [5 × 3] + [(-3) × (-5)]

= 15 + 15

= 30

Now for finding the vector product,

(5î - 3ĵ) × (3î - 5ĵ)

= (5 × -5)î + (3 × -3)ĵ

= -25î - 9ĵ

Therefore,

• Scalar product = 30
• Vector product = -25î - 9ĵ

KNOW MORE:

While calculating the vector product we can apply the determinant method and find out the cross product.