m

Task 2\ (i)

,[mr]

is divided into four line segments of equal length by the points

n,p

and

q

.\ Given that

m=([-2],[r])

and

q=([7],[n])

express

p

and

r

in the form

([a],[b])

.\ (ii) Given the

3D

vectors

p=([4],[0.5]);q=([2],[3]);v=([-6],[1]);w=([-2],[3])

and the scalars\

\\\\lambda _(1)

and

\\\\lambda _(2)

such that

l_(1)=q+\\\\lambda _(1)p

and

l_(2)=w+\\\\lambda _(2)v

. Find the point of intersection of\ these two lines.

(i) [mr] is divided into four line segments of equal length by the points n,p and q. Given that m=(22) and q=(79) express p and r in the form (ab). (ii) Given the 3D vectors p=(40.5);q=(23);v=(61);w=(23) and the scalars 1 and 2 such that l1=q+1p and l2=w+2v. Find the point of intersection of these two lines