NIMCET 2021 — Mathematics PYQ

Let the origin be $O(0,0,0)$. The position vectors of the vertices $A$ and $B$ are given as:

2. Understand the Median through $O$

The median through vertex $O$ is the vector that connects $O$ to the midpoint of the opposite side $AB$. Let this midpoint be $M$.

3. Calculate the Position Vector of Midpoint $M$

The position vector of the midpoint $M$ of a line segment joining two points $A$ and $B$ is given by the average of their position vectors:

4. Perform the Vector Addition

Substitute the given values into the formula:

Combine the components:

5. Find the Final Vector $\overrightarrow{OM}$

Now, divide the result by 2 to find the median:

Conclusion

The vector representing the median through $O$ is $-\hat{j}+\hat{k}$.

Correct Option: (b) $-\hat{j}+\hat{k}$