Analytic Geometry Answers

Determine the vector product (i times i)

Find the radius and the centre of the circle x^2+y^2+z^2-x+z-2=0, x+2y-z=4

How to solve this question'
Find the equation of a line perpendicular to y
4x 3, passing through the point (2, 7)

Find a centre and the principal axes of the following conicoid. Is it ellip-
soids, hyperboloids or something else?
3x2 + 5y2 + 3z2 + 2yz + 2zx + 2xy - 4x - 8z + 5 = 0

Show that the point (0,3+√5) lies on the ellipse with foci (2,3) and(-2,3) and semi-major axis 3.

Suppose that the coordinates of R be (3,4,12), what are the direction cosines of
(
O
R
)
(OR) ƒ—?

3x2 − 4y2 + 6x + 24y − 135 = 0

Let y^2=4ax be a parabola and P be a point on it. Let the normal at P intersect the X-axis at Q. Draw a line at Q perpendicular to the above normal. Show that this line intersects the parabola y^2+4a(x-2a)=0