Table of Contents

- 1 Can the scalar product of two vectors be zero?
- 2 Under what condition is the scalar product of two non zero vectors is zero?
- 3 Can a physical quantity be called a vector if its magnitude is zero?
- 4 Under what condition is the scalar product?
- 5 What is the condition that two non zero vectors are orthogonal?
- 6 What are the maximum and minimum value of a vector dot B vector?
- 7 What are the properties of dot product of vectors?
- 8 What is the difference between dot product and cos product?

## Can the scalar product of two vectors be zero?

Generally, whenever any two vectors are perpendicular to each other their scalar product is zero because the angle between the vectors is 90◦ and cos 90◦ = 0. The scalar product of perpendicular vectors is zero.

## Under what condition is the scalar product of two non zero vectors is zero?

Answer: ≥0 and <90° The scalar product of two nonzero vectors is zero if the angle between the two is_____.

**What does it mean if the product of two vectors is 0?**

If the cross product of two vectors is zero it means both are parallel to each other. Answer: If the cross product of two vectors is 0, it implies that the vectors are parallel to each other. So one of the vectors would be a scalar multiple of the other one.

**Under what conditions the scalar product of two vectors is maximum?**

As one vector approaches the other one’s trajectory, the scalar product increases. Therefore, at angle 0, the scalar product is at its maximum. This can also be seen in the formula, where the product is equal to both of them times cos(angle). Cos(angle) is at its maximum where angle = 0.

### Can a physical quantity be called a vector if its magnitude is zero?

Assertion : A physical quantity cannot be called as a vector if its magnitude is zero. Reason : A vector has both, magnitude and direction.

### Under what condition is the scalar product?

When the two vectors are at at right angle to each other then their scalar product is 0 .

**What is the condition for perpendicularity of scalar product?**

Two vectors A and B are perpendicular if and only if their scalar product is equal to zero.

**What is the condition that two non zero vectors are collinear?**

Two vectors are collinear if their cross product is equal to the zero vector.

## What is the condition that two non zero vectors are orthogonal?

We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.

## What are the maximum and minimum value of a vector dot B vector?

R is maximum when Cos ( A, B) = +1 ie angle between vectors A and B is zero ie vectors A and B are parallel to each other. The resultant of two vector is minimum when both vectors are equal and in opposite direction i.e. the angle between the vector is 180 degrees.

**Is the vector product of two non zero vectors is zero then the vectors must be?**

The dot product of two non zero vectors can only be zero when they are perpendicular to each other and in such a case their cross product becomes maximum or in other words their cross product is equal to the product of their magnitudes. If the dot product is 0 that means they are perpendicular (90 degree angle).

**What is the result of a scalar product of two vectors?**

The result of a scalar product of two vectors is a scalar quantity. Note that if θ = 90°, then cos (θ) = 0 and therefore we can state that: Two vectors, with magnitudes not equal to zero, are perpendicular if and only if their scalar product is equal to zero.

### What are the properties of dot product of vectors?

Dot Product Properties of Vector: Property 1: Dot product of two vectors is commutative i.e. a.b = b.a = ab cos θ. Property 2: If a.b = 0 then it can be clearly seen that either b or a is zero or cos θ = 0 =. It suggests that either of the vectors is zero or they are perpendicular to each other.

### What is the difference between dot product and cos product?

Both the definitions are equivalent when working with Cartesian coordinates. However, the dot product of two vectors is the product of the magnitude of the two vectors and the cos of the angle between them. To recall, vectors are multiplied using two methods

**What is the difference between resultant method and resultant vector method?**

The difference between both the methods is just that, using the first method, we get a scalar value as resultant and using the second technique the value obtained is again a vector in nature.