CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Velocity of a particle is v=6^i+2^j2^k. The component of the velocity parallel to vector a=^i+^j^k in vector form is
  1. 6^i+2^j+2^k
  2. ^i+^j+^k
  3. 2^i+2^j+2^k
  4. 6^i+2^j2^k


Solution

The correct option is C 2^i+2^j+2^k
Given, a vector v  and a unit vector ^n, you can divide the vector v into two parts v=p+q
where  p and q  are parallel and perpendicular to ^n respectively. Now, the magnitude of p is given by p.^n .
Since q.^n=0, we have,
|p|=p.^n=v.^n
thus, 
p=|p|^n=(v.^n)^n
Since the unit vector in the direction of a is given by a|a|, the component of v parallel to a is given by 
(v.a|a|)a|a|=(v.a)a|a|2
So, for the given problem, the component that we get is
(6^i+2^j2^k)(^i+^j+^k)(^i+^j+^k)(^i+^j+^k)(^i+^j+^k)=2^i+2^j+2^k
 

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image