NIMCET 2014 — Mathematics PYQ

1. Given Data:

• $\vec{a}+\vec{b}=\vec{c}$

• $|\vec{a}|=2,|\vec{b}|=2,|\vec{c}|=2$

2. Finding the Dot Product:

We know that for any vector, the square of the magnitude is equal to the dot product of the vector with itself: $\vec{A}\cdot \vec{A}=|\vec{A}{|}^2$.

Taking the dot product of both sides of the equation $\vec{a}+\vec{b}=\vec{c}$ with themselves:

Substitute the given magnitudes (all are equal to $2$):

3. Finding the Magnitude of $(\vec{a}-\vec{b})$:

Now, we calculate the square of the magnitude of the difference:

Substitute the values we know ($|\vec{a}{|}^2=4,|\vec{b}{|}^2=4$ and $2\vec{a}\cdot \vec{b}=-4$):

Taking the square root:

Correct Option: 1 ($2\sqrt{3}$)