Page 78 - Math SL HB Sem 2

6. The line Z passes through the points A (3,2, l) and B (1, 5, 3).

(a) Find the vector AB.

(b) Write down a vector equation of the line Z in the form , = lr + ,r.

The line Z passes through A (0, 3) and B (1, 0). The origin is at O. The point R (x,3 - 3x) is on
I, and (OR) is perpendicular to Z.

(a) Write down the vectors AB and OR .

(b) Use the scalar product to find the coordinates ofR.

8. PointsPandQhavepositionvectors-5i+lU-8kand-4i+9j-5lrrespectively,andbothlie
on a line 21.

(a) (i) Find FQ.

(ii) Hence show that the equation ofZl can be written as

7 = (-J + s) i + (11- 2s)l + (-8 + 3s) k.
(4)

The point R (2, y1, z1) also lies on 21.

(b) Find the value ofyl and o[21.
(4)
The line Z2 has equation t=2i+9 j +l3k + t(i+2 j+3k).

(c) The lines Z1 and 12 intersect at a point T. Find the position vector ofT.
(7)

(d) Calculate the angle between the lines Z1 and 22.
o)

.q Consider tlre points A ( l, 5, 4), B (3, 1, 2) and D (3, ( 2), wittr (AD) perpendicular to (AB).

(a) Find

(i) eE;

(ii) AD, giving your answer in tenns oft.
(3)

(b) Show that ft = 7.
(3)

The point C is such tl,lut eE : I A5.
2

(c) Find the position vector ofC
(4)

(d) Find cos ABC. (3)

3