Analytic Geometry Answers

a = 3i + 2j and b = -4i + 3j, determine B - A

Find the vector equation of the plane determined by the points (0,2,1),(2,1,0),(1,-1,0). Further, check whether the line r=(1+2α)I + (2-3α)j - (1+5α)k intersects this plane. If it intersects, find the point of intersection. If the line and plane do not intersects,find the equation of another line that intersects this plane.

isometries of regular polygon and regular polyedra

Find the radius and the centre of the circular section of the sphere |r|= 4, cut off by the plane r.(2i-j+4k)=3.

Find the vector equation of the plane determined by the points (0,2,1),(2,1,0),(1,-1,0). Further, check whether the line r=(1+2α)I + (2-3α)j - (1+5α)k intersects this plane. If it intersects, find the point of intersection. If the line and plane do not intersects,find the equation of another line that intersects this plane

Identify and trace the conicoid y

2 +z

2 = x. Describe its sections by the planes

x = 0, y = 0 and z = 0.

Obtain the equation of the conic, a focus of which lies at (2,1), the directrix of

which is x+y = 0 and which passes through (1,4). Also identify the conic.

What is the length of the median from point A in a triangle with the the vertices A(5, 7) * B * (7, - 5) and C(- 5, - 1) 

1. Which of the following statements are true and which are false? Give reasons for your

answer. (20)

i) The equation r = acosθ +bsinθ represents a circle.

ii) If 1,1/2,0 are direction ratios of a line, then the line makes an angle of 90◦ with the

x-axis, an angle of 60◦ with the y-axis, and is parallel to the z-axis.

iii) The intersection of a plane and a cone can be a pair of lines.

iv) If a cone has three mutually perpendicular generators then its reciprocal cone has

three mutually perpendicular tangent planes.

Find the value of the acute angle between the lines 3x-y+1=0 and x-2y+1=0.