Question

The velocity of a particle A Va=3i^+4j^.The velocity of another particle B is perpendicular to that of A and has magnitude 5 units.Then Vb ls

Answer 1

both VA and Vb are perpendicular
so their dot product will be zero

Va.Vb=0

3i+4j.xi+yj=0
3x+4y=0. (I)

magnitude of Vb is 5
so, √x*2+y*2=5
x*2+y*2=25. (ii)

from i nd ii we will get the ans

Answer 2

Answer:

The answer is 4i - 3j and -4i + 3j. They have the same line of action but are in opposite directions.

Explanation:

We know that Va = 3i + 4j

Let's consider the unknown vector as

Vb = xi + yj

When you test the perpendicularity of two vectors, you set their dot product equal to zero.

This implies,

3x + 4y = 0

We also want the magnitude of this vector to be 5.

That is,

√(x^2 + y^2) = 5

Solving these two simultaneous equations, we find two alternatives,

4i - 3j and -4i + 3j

And both of them are correct and are the correct answers.

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