Q4 of 181 Page 1217

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


To find angle in Cartesian form, for standard equation of planes



(i)On comparing with the standard equation of planes






(ii)On comparing with the standard equation of planes






(iii) On comparing with standard equation of planes






(iv)On comparing with the standard equation of planes






More from this chapter

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2

Show that the following planes are at right angles:

(i) and


(ii) and


3

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

(i) and


(ii) and


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


 6

Prove that the plane 2x + 2y + 4z = 9 is perpendicular to each of the planes x + 2y + 2z – 7 = 0 and 5x + 6y + 7z = 23.