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A bird is at a point P(4,-1,5) and sees ...

A bird is at a point `P(4,-1,5)` and sees two points `P_(1)(-1,-1,0) " and " P_(2)(3,-1,-3)` . At time t=0 , it starts flying with a constant speed of 10ms to be in line with points `P_(1) " and " P_(2)` in minimum possible time t. Find t, if all coordinates are in kilometers.

Text Solution

Verified by Experts

The correct Answer is:
`3.5 s`
Vector `vec(PP)_(1)=-5hat(i)-5hat(k)` and `vec(P_(1)P_(2))=4hat(i)-3hat(k)`

Let angle between these vectors be `theta` then
`cos theta=((-5hat(i)-5hat(k)).(4hat(i)-3hat(k)))/((5sqrt(2))(5))=-1/(5sqrt(2))`
as `PM=PP_(1) sin theta`
so `PM=(5sqrt(2))(7/(5sqrt(2)))=7m`
Therefore `t=(7m)/(2m//s)=3.5 s`
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