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MathematicsClass XIIJEE Main - EngineeringL2

QUESTION 1

QUESTION BYRamesh Chandra

IIT Kanpur Faculty | Mathematics & Physics | JEE Main & Advanced | 15+ Years Teaching Experience

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Matrix Match No 1

QUESTION

For real numbers 𝛼, 𝛽, 𝛾, 𝛿 and 𝜇 , consider the matrix

(\begin{matrix} α & \frac{1}{\sqrt{2}} & - \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & β & \frac{1}{\sqrt{3}} \\ γ & δ & μ \end{matrix})

. Suppose that 𝑀𝑀𝑇= 𝐼 , where 𝑀𝑇 is the transpose of the matrix 𝑀, and 𝐼 is the 3×3 identity matrix. Let

u \to = α i + \frac{1}{\sqrt{3}} j + γ k

v \to = \frac{1}{\sqrt{2}} i + β j + δ k

and

w \to = - \frac{1}{\sqrt{2}} i + \frac{1}{\sqrt{3}} j + μ k

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List I

The value of $γ^{2} + δ^{2}$ is
If $x u \to + y v \to + z w \to = j$ for some real numbers 𝑥, 𝑦 and 𝑧, then the value of 𝑥 is
The value of $| u \to \cdot (v \to \times w \to) |$ is
The value of $| u \to \times (v \to \times w \to) |$ is

List II

0
1
$\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{3}}$
$\frac{5}{6}$

Your response

Choose the correct matching combination

P → (5) Q → (4) R → (2) S → (1)

P → (4) Q → (5) R → (1) S → (2)

P → (5) Q → (3) R → (2) S → (1)

P → (5) Q → (4) R → (1) S → (2)

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