MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Katrina Tumolva Grade: Upto college level
        

Find the shortest distance from (6,-4,4) to the line joining (2,1,2) and (3,-1,4).

8 years ago

Answers : (1)

AskiitianExpert Shine
10 Points
										

Hi


Find the vector equation of the line joining pt (2,1,2) & (3,-1,4) using r(t) = a + t (b - a ). hence eq wud be r =(2,1,2) +t(1, -2,2).


Suppose the position vector of P from the origin O is OP = p = (6,-4,-4).



The shortest distance of P from L is given by the length of the perpendicular from P to L. Suppose this perpendicular meets L at H. Then we want to find the length of PH. 


  Using the dot product


Since H lies on L we can say that   OH = h = (2,1,2) +t(1, -2,2). = (2+t , 1-2t , 2+2t)

for some value of t which we need to find.

Also, vector PH = -p + h = -(6 , -4, -4) + (2+t , 1-2t , 2+2t)  = (t-4, 5-2t, 6+2t)


But PH is perpendicular to the direction vector (1, -2,2) of line L.

So the dot product of vector PH and (4, 1, -2) is zero.

So t-4, 5-2t, 6+2t).(1, -2,2) =  0   so   solve for t, and find pt h, then find the distance between the two points.

8 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
  • Statistics and Probability
  • OFFERED PRICE: Rs. 636
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details