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