If A=(1,3,-5) and B=(3,5,-3), then the vector equation of the plane passing through the midpoint of AB and perpendicular to AB is

r . (^i +^j +^k) = 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

r . (^i +^j -^k) = 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r . (^i -^j +^k) = 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

N o n e

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $r . (^i +^j +^k) = 2$
$- - \to A B = - - \to O B - - - \to O A = (3^i + 5^j - 3^k) - (^i + 3^j - 5^k) = 2^i + 2^j + 2^k$
Midpoint of AB is (2, 4, -4)
Vector equation of the plane is $[r - (2^i + 4^j - 4^k)] . (2^i + 2^j + 2^k) = 0$
$\Rightarrow r . (^i +^j +^k) = 2 + 4 - 4 \Rightarrow r . (^i +^j +^k) = 2$

Suggest Corrections

Similar questions

Q. If A=(1,3,-5) and B=(3,5,-3), then the vector equation of the plane passing through the midpoint of AB and perpendicular to AB is

Q. The equation if the plane passing through the point (2,-1,3) and perpendicular to the vector

3^i + 2^j -^k

is:

Q. The Cartesian equation of the plane passing through A and perpendicular to

¯ A B

where

3 i + j + 2 k, i - 2 j - 4 k

are the position vectors of A,B respectively

C divides AB in the ratio 5 : 4. If A is (2, 7 ) and B(-3,-8) find the coordinators of C. Find the equation of the line perpendicular to AB passing through C.

Join BYJU'S Learning Program

If A=(1,3,-5) and B=(3,5,-3), then the vector equation of the plane passing through the midpoint of AB and perpendicular to AB is

The correct option is A r.(^i+^j+^k)=2−−→AB=−−→OB−−−→OA=(3^i+5^j−3^k)−(^i+3^j−5^k)=2^i+2^j+2^k Midpoint of AB is (2, 4, -4) Vector equation of the plane is [r−(2^i+4^j−4^k)].(2^i+2^j+2^k)=0 ⇒r.(^i+^j+^k)=2+4−4⇒r.(^i+^j+^k)=2