Question

if 2 vectors p=ai+5j and Q=bi+5j are equal then the correct relation between a and b is?​

Answer 1

For two vectors to be equal it is necessary that their magnitude as well as direction must be equal.

The two given vectors are;

P = ai+5j and Q = bi+5j

For equal vectors, |P| = |Q|

=> √(a^2 + 5^2) = √(b^2 + 5^2)

=> a^2 + 25 = b^2 + 25

=> a^2 = b^2

=> a = ±b

since, direction of P and Q must be same, therefore a ≠ -b.

=> a = +b

Hence, the relation between a and b for the two vectors to be equal is a = +b.

Answer 2

Given :  2 vectors p=ai+5j and Q=bi+5j are equal.

To Find : Correct relation between a and b.

Solution :

For two vectors to be equal it is necessary that their magnitude as well as direction must be equal.

The two given vectors are;

P = ai+5j and Q = bi+5j

For equal vectors, |P| = |Q|

$\[\sqrt {({a^2} + {5^2})} = \sqrt {({b^2} + {5^2})} \]$

 $\[{a^2} + 25 = {b^2} + 25\]$

 $\[{a^2} = {b^2}\]$

 a = ±b

since, direction of P and Q must be same, therefore a ≠ -b.

 a = +b

The relation between a and b for the two vectors to be equal is a = +b.

Hence, The relation between a and b for the two vectors to be equal is a = +b.