Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

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
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)

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

## Other Related Questions on Vectors

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details
• Statistics and Probability
• OFFERED PRICE: Rs. 636
• View Details

Have any Question? Ask Experts

Post Question