Q3 of 181 Page 1217

Find the value of λ for which the given planes are perpendicular to each other:

(i) and


(ii) and


For planes perpendicular Cos90°=0

(1)


(i)On comparing with the standard equation of a plane




2.3 + (-1).2 + (-λ).2=0


6-2-2λ=0


2λ=4


λ=2


(ii) On comparing with the standard equation of a plane




λ.1 + 2.2 + 3.(-7)=0 λ + 4-21=0 λ=17


More from this chapter

All 181 →
1

Find the acute angle between the following planes :

(i) and


(ii) and


(iii) and


(iv) and


2

Show that the following planes are at right angles:

(i) and


(ii) and


4

Find the acute angle between the following planes:

(i) 2X – y + z = 5 and x + y + 2z = 7


(ii) x + 2y + 2z = 3 and 2x - 3y + 6z = 8


(iii) x + y - z = 4 and x + 2y + z = 9


(iv) x + y - 2z = 6 and 2x - 2y + z = 11


 5

Show that each of the following pairs of planes are at right angles:

(i) 3x + 4y - 5z = 7 and 2x + 6y + 6z + 7 = 0


(ii) x - 2y + 4z = 10 and 18x + 17y + 4z = 49