Analytic Geometry Answers

Find the vector equation of the plane determined by the points (1, 0, −1),
(0, 1, 1) and (−1, 1, 0). Also nd the point of intersection of the line

Determine the equation of line of distance P from the origin

the equations [1,2] + t[3,2] and [7,6] + t[-6,-4] give the same line, as(7,6) is a point on the first line,and the direction vectors are scalar multiples of each other. give a third equation that generates the same line.write another two different ewuations that give the same line as each other. include a langraph of your lines

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