Math Is Fun Forum

The topic is called Lines in the Plane and in Space...

1. Submarine A is at (2,4) and fires a torpedo with velocity vector [ 1 ,-3] (i can't do it vertically so i hope you can understand the vectors) at exactly 2.17 pm.
Sunmarine B is at (11, 3) and has velocity vector (-1, a). It fires a torpedo 2 minutes later to intercept the torpedo from A. Given that the interception occurs:
a Find x(t) and y(t) for submarine A
b Find x(t) and y(t) for   "     "      B
c At what time does the interception occur?
d What was the direction and speed of the interception torpedo?

2. Trapezium (trapezoid) KLMN is formed by these lines:
Line 1 (KL) is [x, y] = [2, 19] + p[5, -2]
Line 2 (ML) is [x, y] = [33, -5] + q[-11, 16]
Line 3 (NK) is [x, y] = [3, 7] +r[4, 10]
Line 4 (MN) is [x, y] = [43, -9] + s[-5, 2]
where p, q, r and s are scalars. Lines 1 and 2 meet at L(22,11). Lines 1 and 3 meet at K, Lines 2 and 4 meet at M, lines 3 and 4 at N.

a. Which two lines are parallel? Why?
b. Which lines are perpendicular? Why
c. use vector methods to find the coordinates of K, M and N.
d. Calculate the area of trapezium KLMN.

3. For A(3, -1, 1) and B(0, 2, -1), find the:
a Vector equation of the line passing through A and B
b The coordinates of P which divides BA in the ratio 2:5

4. Find the coordinates of the foot of the perpendicular from Q(-1, 2, 3) to the line x = 2 - t, y = 3 + t, z = -2t.

That's it...really thanks if you do it for me !!

jlo~