Find the equation of plane which passing through the given

Question

Section A

Q.1 If the equation of line ab is (3-x)/1 = (y+2)/(-2)= (z-2)/4 then write the direction ratios of line parralal to above line

Q.2 If the Cartesian equation of a line is (3-x)/5 = (y+4)/7=(2z-6)/4 then find the vector equation for the line?

Q.3 Find the distance of the plane 3x-4y+12z =3 from origin?

Q.4 If x^2/3 + y^2/3 = a^2/3 then find dy/dx?

Section B

Q.5 If then find [A'] ?

Q.6 write a unit vector in the direction of vetor PQ, where vector P and Q are the points ( 1,3,0) and (4,5,6) respectively?

Q.7 find the direction cosines of the line (x+2)/2 = (2y-7)/6 = (5-z)/6 also find the vector equation of the line through the point A(-1,2,3) and parallal to given line?

Q.8 Verify Rolle ‘s theorem for the function f(x) = sinx + cosx , x?[0,π/2

Section C

Q.9 The function

Is continuous on (0, 10) find the value of a and b?

Q.10 Find the points the curves 9y² = x³ where the normal to the curve makes equal intercept on the axes?

OR

Find the approximate value of (3.02) upto 2 places of decimals where f(x) = 3x² + 15x +3?

Q.11 - Solve the set of equation s

X+2y - 3z = -4
2x + 3y + 2z = 2
3x-3y-4z = 11.

Q.12 -Using properties of determinant show that = 9b²(a+b).

Q.13- Find the equation of plane which passing through the points (3,2,0) and contains the line

(x-3)/1 = (y-6)/5 = (z-4)/4 ?

Section D

Q.14 Find the distance of the points (-1,-5,-10) from the points of the intersection of the line r = 2i - j + 2k + λ(3i + 4j+12k) and the plane r.(i- j +k ) = 5

Q.15 - Find two positive numbers x and y such that x+y = 60 and xy³ ix maximum?

Q.16 A housewife wishes to mix together two kinds of food , X and Y in such a way that the mixture contains atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of 1 kg of food are given below.

	Vitamin A	Vitamin B	Vitamin C
Food X	1	2	3
Food y	2	2	1

1 kg of food X costs RS 6 and 1 kg 0f food Y costs Rs 10. Formulate the above problem as a linear programming problem and find the least cost of the mixture which will produce the diet graphically. what value will you like to attach with the problem?