The points A and B have position vectors 7i - 8j + 7k and 4i + 7j + 4k respectively, and O is the origin.?

Question

(i) Find, in vector form, an equation for the line passing through A and B.

I can't seem to get the answer. The given one is r = (7 -8 7) + t(1 -5 1)

(ii) Find the position vector of the point P on the line AB such that OP is perpendicular to AB.

(iii) Show that the line R - (8i - 5j +2k) + λ(i - 10j +4k) does not intersect the line AB.

Answer 1

The dc's of line will be:3,-15,3
Thrfor equatiuon of line is:
r:7i-8j+7k+k(3i-15j+3k)
U shud chek out such questions in RD sharma.Thr r many for practicing.It is a bit difficult to xplain on computer.ur answer is not possible at all.

Answer 2

x=xo+u1*t
y=yo+u2*t
z=zo+u3*t

(xo,yo,zo) can be taken as (7,-8,7)

Direction vector:

(u1,u2,u3)=(7-4,-8-7,7-4)
=(3,-15,3)
=(1,-5,1)

Hence
r = (7 -8 7) + t(1 -5 1)