Home
Class 12
MATHS
A plane is at a distance of 5 units from...

A plane is at a distance of 5 units from the origin and perpendicular to the vector `2hat(i) + hat(j) + 2hat(k)`. The equation of the plane is a)`vec(r ).(2hat(i) + hat(j) -2hat(k))=15` b)`vec(r ).(2hat(i)+ hat(j)-hat(k))=15` c)`vec(r ).(2hat(i) + hat(j)+ 2hat(k))=15` d)`vec(r ).(hat(i) + hat(j) + 2hat(k))=15`

A

`vec(r ).(2hat(i) + hat(j) -2hat(k))=15`

B

`vec(r ).(2hat(i)+ hat(j)-hat(k))=15`

C

`vec(r ).(2hat(i) + hat(j)+ 2hat(k))=15`

D

`vec(r ).(hat(i) + hat(j) + 2hat(k))=15`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

The distance between the line vec(r) = (2hat(i) + 2hat(j) - hat(k)) + lambda(2hat(i) + hat(j) - 2hat(k)) and the plane vec(r).(hat(i) + 2hat(j) + 2hat(k)) = 10 is equal to

Find a vector of magnitude 6 and perpendicular to both vec(a) = 2hat(i) + 2hat(j) + hat(k) and vec(b) = hat(i) - 2hat(j) + 2hat(k)

If 3hat(i) + 2hat(j) -5hat(k)= x(2hat(i) -hat(j) + hat(k)) + y(hat(i) + 3hat(j)-2hat(k))+z(-2hat(i) + hat(j)-3hat(k)) , then

If a + b and a - b are perpendicular and b = 3hat(i) - 4hat(j) + 2hat(k) , then |a| is equal to

If the vectors vec(a) = 2hat(i) + hat(j) + 4hat(k), vec(b) = 4hat(i) - 2hat(j) + 3hat(k) and vec(c) = 2hat(i) - 3hat(j) - lambda hat(k) are coplanar, then findvalue of lambda

The point of intersection of the line vec(r)=7hat(i)+10hat(j)+13hat(k)+s(2hat(i)+3hat(j)+4hat(k)) and vec(r)=3hat(i)+5hat(j)+7hat(k)+t(hat(i)+2hat(j)+3hat(k)) is :

If the vectors 4hat(i) + 11hat(j) + m hat(k), 7hat(i) + 2hat(j) + 6hat(k) and hat(i) + 5hat(j)+ 4hat(k) are coplanar, them m is equal to .