Question

(1) Which of the following function is orthogonal to each other?
(i) /y2y2dı = 0
(ii) Jyly2dt = 0
ilyly2dt = 1
(iv) ſw2w2dt = 1.​

Answer 1

Explanation:

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11th

Physics

Work, Energy and Power

Scalar Product

If vectors A = cos ω t î +...

PHYSICS

If vectors A=cosωt

i

^

+sin

j

^

and B=cos

2

ωt

i

^

+sin

2

ωt

j

^

are functions of time, then the value of t at which they are orthogonal to each other

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ANSWER

Given,

A

=(coswt

i

^

+sinw

j

^

)⋅

B

=(cos

2

wt

i

^

+sin

2

wt

j

^

)

When they are orthogonal, their dot product will e zero

A

⋅

B

=(coswt

i

^

+sinwt

j

^

)⋅(cos

2

wt

i

^

+sin

2

wt

j)

0=cos(wt−

2

wt

)

cos(wt−

2

wt

)=0=

2

π

cos(

2

wt

)=

2

π

2

wt

=

2

π

t=

w

π

Hence, value of time is

ω

π