Question

If two vectors are perpendicular to each other then which of these is zero

(a) scalar product or dot product (b) vector product or cross product

(c) both (a) and (b) (d) non​

Answer 1

If two vectors are perpendicular to each other then their scalar product or dot product is zero.

• The scalar product of two vectors:

Let us take two vectors A→ and B→ and the angle between them be α.

The scalar product or dot product is the product of the magnitude of the two vectors and the cos of the angle between them:

Therefore in this case dot product of the two vectors = |A||B| cosα

Since in this case α = 90°

∵ cos 90° = 0

Dot product = |A||B| *0 = 0

• While the cross product would be |A||B| sin α which will not be 0 when both vectors are perpendicular.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If two vectors are perpendicular to each other then which of these is zero

(a) scalar product or dot product

(b) vector product or cross product

(c) both (a) and (b)

(d) none of the these

CONCEPT TO BE IMPLEMENTED

SCALAR PRODUCT OR DOT PRODUCT

Let two vectors are $\vec{a} \: \: and \: \: \vec{b}$

Also let $\theta$ be the angle between them.

Then their dot product is denoted by

$\vec{a} \: . \: \vec{b}$ and defined as

$\vec{a} \: . \: \vec{b} = | \vec{a}| | \vec{b}| \cos \theta$

EVALUATION

Here it is given that two vectors are perpendicular to each other

Let $\vec{a} \: \: and \: \: \vec{b}$ are the given two vectors and

$\theta$ be the angle between them

$\therefore \: \: \vec{a} \: . \: \vec{b} = | \vec{a}| | \vec{b}| \cos \theta$

Then by the given condition

$\displaystyle \theta = \frac{\pi}{2}$

$\therefore \displaystyle \: \vec{a} \: . \: \vec{b} = | \vec{a}| | \vec{b}| \: \cos \frac{\pi}{2}$

$\therefore \displaystyle \: \vec{a} \: . \: \vec{b} =0 \: \: \: ( \because \: \cos \: \frac{\pi}{2} = 0 \: \: )$

Hence scalar product or dot product is zero

FINAL ANSWER

If two vectors are perpendicular to each other then which of these is zero

(a) scalar product or dot product

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