Q20 of 29 Page 1

A plane meets the coordinate axes in A B and C such that the centroid of Δ ABC is the point (α, β, γ). Show that the equation of the plane is

As A, B and C are on the coordinate axes, coordinates of A, B and C will be


A = (a, 0, 0)


B = (0, b, 0)


C = (0, 0, c)


Also, centroid of a triangle joining (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) is




⇒ a = 3α, b = 3β, c = 3γ


Also, equation of a plane with intercept is



Where, a, b and c are x-intercept, y-intercept and z-intercept only


Therefore, Equation of given Plane




More from this chapter

All 29 →
18

Can y = ax + be a solution of the following differential equation?


If no, find the solution of the D.E. (*).


OR


Check whether the following differential equation is homogeneous or not



Find the general solution of the differential equation using substitution y=vx.


 19

If the vectors and are coplanar, then for a, b, c ≠ 1 show that


 21

If a 20-year-old girl drives her car at 25 km/h, she has to spend Rs 4/km on petrol. If she drives her car at 40 km/h, the petrol cost increases to Rs 5/km. She has Rs 200 to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as a Linear Programming Problem. Write any one value reflected in the problem.

 22

The random variable X has a probability distribution P(X) of the following form, where k is some number:


(i) Find the value of k


(ii) Find P(X <2)


(iii) Find P(X ≤ 2)


(iv) FindP(X ≥ 2)