 ×     #### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+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
```
The lines px+qy+r=0 qx+ry+p=0 rx+py+q=0 are concurrent if a)p+q+r=0b)p^2+q^2+r^2=pq+qr+rpc)p^3+q^3+r^3=3pqrd)none of theseAnswer given is a,b,c

```
3 years ago

```							The condition for concurrency of three linesa1x +b1y+c1 = 0,a2x+b2y+c2 = 0 anda3x+b3y+c3=0 isThe determinant|a1 b1 c1||a2 b2 c2||a3 b3 c3|= 0Hence the condition for given lines to be concurrent is|p q r||q r p||r p q|= 0=> p(rq-p²) –q(q²-rp) +r(pq-r²) = 0=> prq - p³ - q³+qrp +rpq - r³ = 0= > -p³-q³-r³ = -3pqr=> p³+q³+r³ = 3pqr=> p³+q³+r³ - 3pqr = 0=> (p+q+r)(p²+q²+r²-pq-qr-rp) = 0=> p+q+r = 0 or=> p²+q²+r² = pq+qr+rp Hence option A, B, C are correct.
```
3 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Analytical Geometry

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 53 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions