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Q:

Which of the following two statements is more appropriate:

A:

Two velocities are added using the triangle rule because velocity is a vector quantity.

Q:

Can you add three unit vectors to get a unit vector ?

Does your answer change if two unit vectors are along

the coordinate axes ?

A:

yes, taking three unit vectors as i , -i and j it sums up to be j which is a unit vector.

No my answer won't change.

Q:

Let A→=3i→+4j→. Write four vector B→ such that A→≠B→ but A=B

A:

so the four different vectors can be

**vec(B) = 3i-4j , -3i+4j, -3i-4j , 5k **

Q:

The dot product of a vector A with the zero vector is

A:

0

Q:

Can you add two vectors representing physical

quantities having different dimensions ? Can you

multiply two vectors representing physical quantities

having different dimensions ?

A:

Addition is not possible.

Multiplication is possible.

Q:

Can a vector have zero component along a line and still

have nonzero magnitude ?

A:

Yes.

For example = 2i +0j

has magnitude of 2 along x direction.

Q:

Can we have physical quantities having magnitude and

direction which are not vectors ?

A:

It also should follow vector law of addition

No. A physical quantity having both magnitude and direction need not be considered a vector. For example, despite having magnitude and direction, current is a scalar quantity.

Q:

Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is

A:

0

Q:

Is it possible to add two vectors of unequal magnitudes

and get zero ?

A:

No.

Let the two vectors you want to add be A→ and B→.

We want A→+B→=0

So, A→=0→−B→

which means A→=−B→

Taking the magnitudes

|A→|=|−B→

So,|A→|=|B→|

This means the two vectors have to be equal in magnitude and opposite in direction in order to cancel out.

Q:

In which case vector product and cross product will be equal?

A:

All

Q:

A vector A points vertically upward to the plane and B points towards north. The vector product A

× B is

A:

Along west

Q:

Is a vector necessarily changed if it is rotated through

an angle ?

A:

Yes. A vector is defined by its magnitude and direction, so a vector can be changed by changing its magnitude and direction. If we rotate it through an angle, its direction changes and we can say that the vector has changed.

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