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If f (alpha) =x cos alpha + y sin alpha ...

If `f (alpha) =x cos alpha + y sin alpha - p (alpha),` then the lines `f (alpha)=0 and f (beta)=0` ar perpendicular to each other, if

A

`alpha = beta`

B

`alpha + beta =(pi)/(2)`

C

`|alpha - beta| =(pi)/(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • Let F(alpha)=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,0,1)] then F(alpha), F (beta) is equal to

    A
    `F(alpha beta)`
    B
    `F((alpha)/(beta))`
    C
    `F(alpha+beta)`
    D
    `F(alpha-beta)`

  • If the lines x(sin alpha+sin beta)-y sin(alpha-beta)=3 and x(cos alpha+cos beta)+ycos (alpha-beta)=5 are perpendicular then sin alpha+sin 2 beta=

    A
    `sin(alpha-beta)-2sin(alpha+beta)`
    B
    `sin2(alpha-beta)-2sin(alpha+beta)`
    C
    `2sin(alpha-beta)-sin(alpha+beta)`
    D
    `sin2 (alpha-beta)-sin(alpha+beta)`

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