Hosam

The matrix A =

5, 4, a

a, 3, 2

2, 1, 1

what value(s) of variable a will make the determinant equal to zero....??

Matrix A is given by

1 0 a

1 -1 3

2 b 1

Find the values of a and b that will make det(A) = 0.

The plane contains the whole line L which is given by

(x, y, z) = (5, 1, 2) + t (3, -2, 4)

And also contains the point (1, 2, 3).

the spherical coordinates of B are (1, pi/3, pi/3), then what

are the possible spherical coordinates of point C, such that

the points A, B and C form an equilateral triangle.

Note that A, B, and C are on the same sphere. so the first

coordinate of C is equal to 1 (the radius of the sphere).

Also note that the second coordinate above is (theta), the angle

between the position vector of a point and the z-axis. And the third coordinate (phi) is the angle between the projection of the position vector onto the xy-plane and the x-axis.

First sphere centered at (1,1,1) and has a radius of 10

Second sphere centered at (5, 7, 13) and has a radius of 8.

The first circle has a radius of 4 and is centered at (1, 3).

The second circle has a radius of 3 and is centered at (4, 7).

A walker and a jogger left the town of Pi at the same time, heading toward the town of Epsilonville. The walker and jogger travel at constant speeds of 6 km/h and 10 km/h, respectively.

At the same time, a biker left Epsilonville, heading toward the town of Pi. The biker travels at a constant speed of 14 km/h.

If the biker passed the walker 4 minutes after passing the jogger, how far apart are the towns Pi and Epsilonville?

each of the three vectors.

5 x^2 + 6 y^2 + 7 z^2 + 4 xy + 4 yz - 40 x - 80 y - 62 z + 37 = 0

Find it's center, and the length and orientation of its axes.

whose equation is n . ( r - r0) = 0, where r0 is a point on the plane and n is a normal vector to the plane. (n is not necessarily a unit vector).

Then use the transformation you derived to find the transformed equation of the line

L: r = (1, 1, 1) + t (-1, 0, 1)

After reflecting across the plane 2x - y + 3z = 1.

Find all solutions in [0, 2pi]

radius of base R.

Find the transformed equation of the line x - 2y + 1 = 0

after it gets reflected about the line y = 2x - 3.

A coffee merchant mixes two types of beans, bean (1) and bean (2), to make different blends of coffee. All of these blends are sold at the same price.

If he mixes bean (1) and bean (2) in the ratio (by weight) 2 : 1, then he makes a profit of 26%.

If he mixes bean (1) and bean (2) in the ratio (by weight) 3 : 2, then he makes a profit of 20%.

In what ratio should he blend bean (1) and bean (2) for his profit to be 40%?

Assume that the line L is given in parametric form as (x,y,z) = r0 + t d, where r0 = (x0, y0, z0), and

d = (dx, dy, dz) is the direction vector of the line. The rotation affects any point in space (x, y, z)

and rotates it about the line L by an angle A, in a right hand sense i.e. if the thumb points along the direction vector d, then the fingers indicate the direction of rotation. You may assume that the vector d is a unit vector.