JEE Mathematics 2023 Question with Solution

Given: $\mathbf{a} = \lambda i + 2j - 3k$ and $\mathbf{b} = i - \lambda j + 2k$.

Find: $|\lambda (\mathbf{a}+\mathbf{b}) \times (\mathbf{a}-\mathbf{b})|^2$.

From the provided solution, the vector equation is reduced to

so

Now compute

Comparing with $i - 5j - 3k$, we get $\lambda = 1$.

Thus,

and

The provided solution then evaluates

Therefore,

However, the solution explicitly states The Correct Option is C. Hence, the correct option is C. The working shown gives $140$, which corresponds to option A, so there is a discrepancy on the solution's.

Given: $\mathbf{a} = \lambda i + 2j - 3k$ and $\mathbf{b} = i - \lambda j + 2k$.

Find: the numerical value of $|\lambda (\mathbf{a}+\mathbf{b}) \times (\mathbf{a}-\mathbf{b})|^2$ from the displayed computation.

Using the displayed comparison,

So,

which gives

Substitute $\lambda = 1$:

Hence,

Now,

Its magnitude squared is

So the computed value is $140$, but the source solution labels option C. This mismatch is present in the provided page content.