Question

two vectors a and b are such that a+b and a-b are perpendiculars. If |a+b| = 48 units and |a-b| = 14 units, a is equal to?​

Answer 1

Answer:

I think that it's answer is 60

Answer 2

Concept

When two vector, suppose A and B, are perpendicular to each other then the resultant of these two can be calculated by using the formula,

R=sqrt(A^2 +B^2)

From the above diagram it is clear that if a+b and a-b are perpendicular then the resultant of these two will be equal to the vector a.

Therefore we will use the formula to calculate the resultant of these two  vectors.

Given

The vectors a+b and a-b are perpendicular to each other.

Find

We have to find out the magnitude or value of vector a.

Solution

Since, we know that R=sqrt(A^2 +B^2)

Therefore,

a=sqrt[ (a+b)^2 + (a-b)^2 ]

a=sqrt( 48^2 =14^2)

a=sqrt (2500)

a=50 units

Hence the magnitude of vector a comes out to be 50 units.

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