If A, B and C are the unit vectors along the incident ray, reflected ray and the outward normal to the reflector. Then which of the following options is correct?
A)B=A-C
B)B=A+(A.C)C
C)B=2A-C
D)B=A-2(A.C)C
Answers
Given: a, b and c are the unit vectors along the incident ray, reflected ray and the outward normal to the reflector.
To find: The correct option from the given choices?
Solution:
- Let the angle of incidence is α.
- Now we have given that a is the unit vector along the incident ray.
- So, the vector form will be: sin α (i) - cos α (j) ...........(1)
b is the unit vector along the reflected ray.
- So the vector form will be: sin α (i) + cos α (j) ..........(2)
- Now lets subtract 1 from 2, we get:
b(vector) - a(vector) = sin α (i) + cos α (j) - ( sin α (i) - cos α (j) )
= sin α (i) + cos α (j) - sin α (i) + cos α (j)
= 2 cos α (j) ................(3)
- Now dot product of a and c vector is:
a . c = IaI x IcI cos (180 - α)
But IaI x IcI = 1
So, a.c = - cos α
cos α = -a.c ..............(4)
- Putting 4 in 3, we get:
b(vector) - a(vector) = 2 (-a.c) (j)
b(vector) = a(vector) - 2 x a.c (j)
- But j(vector) = c(vector) because value is same, so:
b(vector) = a(vector) - 2 x a.c (c)
Answer:
So the correct option is b(vector) = a(vector) - 2 x a.c(c) (4th option)
Answer:
Hii mate
Step-by-step explanation:
option C is correct ( B=2A-C )