JEE Mathematics 2023 Question with Solution

Given: $\overrightarrow{AB} = -2\hat{i} + \hat{j} + 3\hat{k}$, $\overrightarrow{CA} = 4\hat{i} + 3\hat{j} + 4\hat{k}$, and area of triangle ABC is $5\sqrt{6}$.

Find: The required value asked in the options.

From the solution working, let the third component be $\delta$ and write

Then

So,

Using area of triangle,

Hence,

Therefore,

Squaring both sides,

So $\delta = 5$.

Then

Now,

Thus the working gives the value $60$. However, the solution explicitly marks Option A as correct, while the answer key marks (2). Since the solution is the primary source, the correct option is taken as A.

The extracted question text appears corrupted: it states $\overrightarrow{CB} = \hat{i} + \hat{j} + \hat{k}$ in the question, but the solution recomputes $\overrightarrow{CB}$ using an unknown third component $\delta$ and finally evaluates a dot product equal to $60$.

So there is a mismatch between the displayed question, the option values, and the conclusion in the solution. The numerical result obtained from the worked solution is $60$, which corresponds to Option B, but the solution says The Correct Option is A. Following the instruction that the solution is the primary source, the recorded answer is A, while preserving the discrepancy here.