Question

A vector P is directed along x direction. What is P.P?
MCQ!!

Zero

One

P²

2P
​

Answer 1

Given:

Vector P is directed along X direction.

To find:

Scalar product between vector P and vector P.

Diagram:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(3,2){\vector(0,1){3}}\put(2,3){\vector(1,0){3}}\put(3,4){\vector(1,0){2}}\put(4,4.25){ \vec{P} }\put(5.25,3){x}\put(3,5.25){y}\end{picture}}$

Calculation:

As per the question , vector P can be represented as follows:

$\vec{P} = ( P) \: \hat{i}$

Now , required scalar product;

$\therefore \: \vec{P} \: . \: \vec{P} = (P) \: \hat{i} \: . \: (P) \: \hat{i}$

$= > \: \vec{P} \: . \: \vec{P} = (P) \times (P)$

$= > \: \vec{P} \: . \: \vec{P} = {(P )}^{2}$

So, final answer is:

$\boxed{ \sf{\vec{P} \: . \: \vec{P} = {(P )}^{2} }}$

Additional information about Scalar Product:

• It is also known as dot product.

• Scalar product between mutually perpendicular vectors is zero.

• Scalar product between parallel unit vectors is 1.

Answer 2

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