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kkurt [141]
3 years ago
15

Show that (×)× = ×(×) if and only if the vectors and are collinear.

Mathematics
1 answer:
WITCHER [35]3 years ago
3 0

Step-by-step explanation:

<em>NOTE: Bolded letters are vectors</em>

Given that ,

  • (axb)xc = ax(bxc)

From vector triple product rule,

  • ax(bxc) = b(a.c)-c(a.b)
  • ax(bxc) = b(a.c)-a(b.c)

If these both are equal, then :

⇒b(a.c)-c(a.b) = b(a.c)-a(b.c)

⇒(-a.b)c = (-b.c)a

⇒(|a||b|sin∅)c = (|b||c|sinФ)a (cancel |b| on both sides)

A , C are the unit vectors of a and c respectively .

Two vectors can be equal on when their magnitude and directions are same.

That is when ,

⇒(|a||c|sin∅)A = (|a||c|sinФ)C

⇒sin∅A = sinФC

This can only be possible when the vectors are collinear because the angle made by the vectors with the vector B should be the same or supplementary and the vectors A and C must be in the same direction.

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Answer:

1

+

sec

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1

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1

.

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+

1

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2

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x

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⋅

sin

2

(

x

)

1

Combine.

1

+

1

sin

2

(

x

)

cos

2

(

x

)

⋅

1

Multiply  

sin

(

x

)

2

by  

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

⋅

1

Multiply  

cos

(

x

)

2

by  

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

Apply Pythagorean identity in reverse.

1

+

1

−

cos

2

(

x

)

cos

2

(

x

)

Simplify.

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cos

2

(

x

)

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2

(

x

)

Convert to sines and cosines.

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1

2

cos

2

(

x

)

One to any power is one.

1

cos

2

(

x

)

Because the two sides have been shown to be equivalent, the equation is an identity.

1

+

sec

2

(

x

)

sin

2

(

x

)

=

sec

2

(

x

)

is an identity

Step-by-step explanation:

7 0
2 years ago
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Given the differential equation

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