Analytic Geometry Answers

Find the radius of the circular section of the

sphere Ir—cl = 7 by the plane

r. (3i — j + 2k) = 2 ,r7 , where c = (— 1, 0, 1).

A circle and a hyperbola can have a maximum of how many intersection?

The vertices of quadrilateral OPQR are O(0,0), P(2,0), Q(4,2), R(0,3). The vertices of its image under a rotation are O'(1,-1), P'(1,-3), Q'(3,-5) and R'(4,-1).
(a)(i) On the grid draw OPQR and its image O'P'Q'R'.
(ii) by construction determine the centre and angle of rotation.
(b) On the same grid as (a) (i) above, draw O''P''Q''R'', the image of O'P'Q'R' under a reflection in the line y = x
(c)From the quadrilaterals drawn, state the pairs that are:
(i) Directly congruent; (
(ii) Oppositely congruent

A parallelogram is formed in R3 by the vectors = (3, 2, –3) and = (4, 1, 5). The point P = (0, 2, 3). a. Determine the location of the vertices. b. Determine the vectors representing the diagonals. c. Determine the length of the diagonals.

Draw two non-collinear vectors

A parallelogram is formed in R3 by the vectors = (3, 2, –3) and = (4, 1, 5).
The point P = (0, 2, 3).
a. Determine the location of the vertices.
b. Determine the vectors representing the diagonals.
c. Determine the length of the diagonals.

if \\(a=a_{1}i+a_{2}j+a_{3}k\\) and \\(b=b_{1}i+b_{2}j+b_{3}k\\), then ab

The work done in moving an object along a straight line from (3, 2, -1) to (2, -1, 4) in a force field by F=4i-3j+2k\n

A is the point of intersection of the lines 3x − y = 7 and x + 4y + 2 = 0. Find
(a) in normal form, the equation of the line which passes through A and is parallel
to the line 2x + 3y − 40 = 0,
(b) the perpendicular distance of A from the line 2x + 3y − 40 = 0

Find the distances between the following pairs of parallel lines
(a) r · (i + j) + 7 = 0, r · (i + j) − 11 = 0;
(b) r · (2i − 3j) + 6 = 0, r · (4i − 6j) + 5 = 0;
(c) r = i + j + s(4i − j), r = 4i + 5j + t(8i − 2j).