Scalar and Vector Product MCQ Quiz in मल्याळम - Objective Question with Answer for Scalar and Vector Product - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

Scalar Product of Two Vectors - 

Vector Product of Two Vectors - 

 is the unit vector perpendicular vector, θ being the angle between   and 

Calculation:

Given

⇒

⇒ cos θ = sin θ

⇒ tan θ = 1

⇒ θ = 

The angle between   and  is 

Calculation:

Given: In the right-angled triangle ABC, hypotenuse AC = p

As we can see from the above diagram angle between vector  is 90° ⇒

Concept:

Vector Triple Product: Vector Triple Product is a vector quantity.

Vector triple product of three vectors a, b, c is defined as the cross product of vector a with the cross product of vectors b and c, i.e. a × (b × c)

a × (b × c) = (a . c) b – (a . b) c

a.b = |a||b|cos θ

Calculation: 

Here, |a| = 1, |b| = 1, |c| = 2

Taking magnitude both sides, we get

4cos² θ |a|² + |c|² - 2 × 2cos θ  = |b|²

4cos2 θ + 4 - 2 × 2cos θ × |a||c|cos θ = 1

4cos2 θ + 4 - 8cos2 θ  = 1

4cos2 θ = 3

cos2 θ = 

cos θ = 

∴ θ = π / 6

Hence, option (2) is correct.

Concept:

For two vectors  and  at an angle θ to each other:

• Dot Product is defined as .
• Cross Product is defined as  where  is the unit vector perpendicular to the plane containing  and .

Calculation:

According to the question:

                 ...(1)

As we know,          

                      ...(2)

Dividing (2) by (1), we get:

tan θ = √3

⇒ θ = .

Concept:

Calculation:

Here, 

Taking magnitude and squaring both sides,

θ = 0°

Hence, option (1) is correct. 

Concept:

a.b = |a||b|cosθ

Calculation: 

Here,   and  

Now, 

Hence, option (3) is correct.

Concept:

• If  are two vectors, then the scalar product between the given vectors is given by: 
• If  then
• If  is a vector then the magnitude of the vector is given by 

Given: 

As we know that, 

As we know that, if  is a vector then the magnitude of the vector is given by 

Concept:

Let  be a vector then

Calculation:

Hence, statement 1 is true.

If cos θ = 1

But if cos θ ≠ 1

Hence, statement 2 is not true .

Hence, statement 3 is true.

Concept:

If vector v = ai + bj + ck, then magnitude of vector v is .

Projection of vector v on c is 

A vector  in the plane of  and  is 

Calculation:

A vector  in the plane of  and  is  

⇒ 

⇒  = 

Projection of  on (given)

⇒ 

⇒             [ = √3]

⇒ 

⇒ 

∴ Vector 

Concept:

I. If  are two vectors, then the scalar product between the given vectors is given by:

II. If  then  is the unit vector perpendicular to both 

Calculation:

Given: 

As we know that, If  then  is the unit vector perpendicular to both 

As we know that, If  are two vectors, then the scalar product between the given vectors is given by: