Physics, asked by akshatagrawal, 1 year ago

if vector a^+2b^ perpendicular to vector 5a^-4b^ find the angle between a^ and b^

Answers

Answered by Anonymous
113

Answer:

The angle formed between the two vectors is 60°

60° is the correct answer.

Explanation:

The two given vectors are

V1 = a^+2b^

V2 = 5a^-4b^

The two vectors are perpendicular to each other

To find: the angle between a^ and b^

Solution:

Let θ be the angle between the two vectors a and b.

We know that angle between two vectors is given by cosθ

Thus,

cosθ = a∙b/a||b|

The vectors a and b are unit vectors as given.

Hence,

|a|=√(1) (1)) =1

|b|=√(1) (1)) = 1.

V1 = a^+2b^ and V2 = 5a^-4b^ are perpendicular as given

Hence,

Dot product of two vectors will be zero

(a^+2b^)( 5a^-4b^) =0

Expanding the brackets we get

5a∙a + 6ab- 8b∙b = 0

6a∙b = 8b∙b - 5a∙a

a and b are unit vectors as given

6a∙b = 8-5 = 3

According to formula

cos θ = 3/6.

cos θ = 1/2

θ = cos ^-1 (1/2)

= 60°

Thus angle formed between the two vectors is 60°

Hence, 60° is the correct answer.

Answered by Dayanandsatkar
17

Answer:

60

Explanation:

CosO=A.B/IAIBI

A.B is the vector while

lAlBl is the magnitude

When we find vector and the magnitude we get 3 by under root 46 which is 3/6= 1/2

Cos 1/2 is 60

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