Vector Equations C4 Question

Hi, can anyone help with this C4 vector question. I done part (a) but i'm not sure so a full solution would be good. Cheers!

Relative to a fixed origin O, the points A and B have position vectors (4i + 3j - k) and (i + 4j + 4k) respectively.

(a) Find a vector equation of the line l1, which passes through A and B.

The line l2 has equation r= 22i + aj + 4k + U(bi - j +2k), where U is a scalar parameter and a and b are constants. Find

(b) The values of a and b

(c) The position vector of the point of intersection of l1 and l2.

Thanks guys.

AK

Reply 1

El Stevo

A = (4i + 3j - k)
B = (i + 4j + 4k)

line = [vector point] + lamda[vector direction]

Direction AB = b - a
Direction AB = (i + 4j + 4k) - (4i + 3j - k)
Direction AB = (-3i + j + 5k)

Point is any point you know on the line, we know A and B, so use either of them....

r = (4i + 3j - k) + [lamda](-3i + j + 5k)