Question

Please ans this Ques from Phy : Vectors (DOT PROD)
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Answer 1

Answer:

( 2 )

Explanation:

Given, dot product of vector sum and vector difference of two vectors is perpendicular.

This means: if two vectors are A and B and angle between their sum and difference is C, then ( A + B )( A - B )cosC = ( A + B )( A - B )cos90° = ( A + B )( A - B )0 = 0

= > ( A - B )( A + B ) = 0

= > A^2 - B^2 = 0

= > A^2 = B^2

This means, both the vectors are equal in magnitude.

Answer 2

Given that,

The sum of two vectors and the difference of two vectors are perpendicular to each other.

We need to find,

the nature of the force.

Solution :-

Let the angle between them be θ.

Here, θ = 90°

We know,

If two vectors are perpendicular then the dot product(scalar product) must be zero.

$(\vec{a}+\vec{b}).(\vec{a}-\vec{b})=0\\\\\implies \vec{a}.\vec{a}-\vec{a}.\vec{b}\ +\ \vec{b}.\vec{a}-\vec{b}.\vec{b}=0 \\\\\implies \vec{a}.\vec{a}-\vec{b}.\vec{b}=0\\\\\\\underline{{As,\vec{a}.\vec{b}=\vec{b}.\vec{a} }}\\\\\\\implies \vec{a}.\vec{a}=\vec{b}.\vec{b}\\\\\implies |\vec{a}|^2= |\vec{b}|^2$

We know, magnitude of a vector cannot be negative. So,

$\boxed{\implies |a|=|b|}$

∴ So, the answer is (2) Are equal to each other in magnitude.