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Let, P=({:(cos""pi/4, -sin""pi/4),(sin""...

Let, `P=({:(cos""pi/4, -sin""pi/4),(sin""pi/4, cos""pi/4):}) " and " x=({:(1/sqrt(2)),(1/sqrt(2)):})`. Then `P^(3)X` is equal to-

A

`({:(0),(1):})`

B

`({:(-1/sqrt(2)),(1/sqrt(2)):})`

C

`({:(-1),(0):})`

D

`({:(-1/sqrt(2)),(-1/sqrt(2)):})`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • Let Q=({:(cos""pi/4,-sin""pi/4),(sin""pi/4, cos""pi/4):}) and X=({:(1/sqrt(2)),(1/sqrt(2)):}) then Q^(3)X is equal to

    A
    `({:(0),(1):})`
    B
    `({:(-1/sqrt(2)),(1/sqrt(2)):})`
    C
    `({:(-1),(0):})`
    D
    `({:(-1/sqrt(2)),(-1/sqrt(2)):})`

  • The least positive integer n such that ({:(cos""((pi)/(4)),sin""((pi)/(4))),(-sin""((pi)/(4)),cos""((pi)/(4))):})^n is an identity matrix of order 2 is

    A
    4
    B
    8
    C
    12
    D
    16

  • The value of int_(-(pi)/(4))^((pi)/(4)) x^(3) sin^(4) x dx is equal to -

    A
    `(pi)/(4)`
    B
    0
    C
    `(pi)/(3)`
    D
    `(pi)/(2)`

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