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).

Vector a= 2i+2j+3k
Vector b=i+2j+k
Vector c= 3i+j
Are such that a+yb is perpendicular to c find y.

What is the equation of line which is pararrel to (3x-2y=5)and passes through the point (-2,-4)

A square has verticles O(0,0), A(a,o), B(a,a) and C(o,a).
Find:
(a) the mid point of the diagonals OB and CA
(b) the length of a diagonal of the square and the radius of the circle in which OABC is inscribed
(c) the equation of the circle inscribing the square.

Prove that in any parallelogram,the sum of the squares of all sides is equal to the sum of the squares of the diagonals

What are the coordinates of the centroid of the triangle with vertices (X1,Y1), (X2,Y2), (X3 ,Y3)

Find the equation of the line which passes through the point (1,√3) and makes anangle of 30◦ with the line x+√3y+√3 = 0.

Show that for any three vector a, b, c
a*(b*c)+b*(c*a) +c*(a*b) =0

line segment AC has endpoints A (-1, -3.5) and C (5,-1). Point B is on like segment AC and is located at (0.2, -3). what is the ratio of AB/BC?