Q14 of 26 Page 1

Find the coordinates of the foot of the perpendicular drawn from the point A( - 1, 8, 4) to the line joining the points B(0, - 1, 3) and C(2, - 3, - 1). Hence find the image of the point A in the line BC.

The Cartesian equation of line passing through A(x,y,z),B(x1,y1,z1) and C(x2, y2, z2) is given by


⇒


B is (0, - 1,3) and C is (2, - 3, - 1)


Substituting the values we get


⇒


⇒


∴ General coordinates of P is (2λ, - 2λ - 1, - 4λ + 3)


Direction ratio of AP(2λ + 1, - 2λ - 9, 4λ - 1)


AP is perpendicular to BC


2(2λ + 1) - 2( - 2λ - 9) - 4( - 4λ - 1) = 0


4λ + 2 + 4λ + 18 + 16λ + 4 = 0


24 + 24λ = 0


λ = - 1


P( - 2,1,7)


∴ Coordinates of Foot of perpendicular are ( - 2,1,7)


Coordinates of image of A is P’(a,b,c) is


⇒


⇒ a = - 3


⇒


⇒ b = - 6


⇒


⇒ c = 10


P’( - 3, - 6,10)


More from this chapter

All 26 →
12

If then prove that

Hence show that



OR


Find if

13

A bag X contains 4 while balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.

OR


A and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.

 15

Show that the four points A (4, 5, 1), B(0, - 1, - 1), C(3, 9, 4) and D( - 4, 4, 4) are coplanar.

 16

A typist charges ₹ 145 for typing 10 English and 3 Hindi pages, while charges for typing 3 English and 10 Hindi pages are ₹ 180. Using matrices, find the charges of typing one English and one Hindi page separately. However, typist charged only ₹ 2 per page from a poor student Shyam for 5 Hindi pages. How much less charged from this poor boy? Which values are reflected in this problem?