The position vectors of three points A,B anc C `(-4hat(i) +2hat(j) -3hat(k))`
`(hat(i) +3hat(j) -2hat(k)) "and " (-9hat(i) +hat(j) -4hat(k))` respectively . Show that the points A,B and C are collinear.

The position vectors of the points A, B and C are 2hat(i)+6hat(j)-hat(k), hat(i)+2hat(j)+4hat(k) " and " 3hat(i)+10hat(j)-6hat(k) respectively. Show that the points A, B and C are collinear.

The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(k), 4hat(i)+5hat(j)+hat(k) " and " 3hat(i)+6hat(j)-3hat(k) respectively. Show that the points form a right-angled triangle.

If the position vectors of the points A, B C are 3hat(i)-4hat(j)-4hat(k), 2hat(i)-hat(j)+hat(k) " and " hat(i)-3hat(j)-5hat(k) respectively. Show that ABC is right-angled triangle.

If the position vectors of the points A, B, C are -2hat(i)+2hat(j)+2hat(k), 2hat(i)+3hat(j)+3hat(k) " and " -hat(i)-2hat(j)+3hat(k) respectively, show that ABC is an isosceles triangle.

(i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k) respectively, then show that the points B bisects the line-segment bar(AC) . (ii) The position vectors of the points P and Q are 5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k) respectively. Find the position vectors of the trisection points of the line-segment bar(PQ) .

The position vectors of A, B, C are 2hat(i)+hat(j)-hat(k), 3hat(i)-2hat(j)+hat(k) and hat(i)+4hat(j)-3hat(k) respectively. Show that A, B and C are collinear.

Show that the points A,B,C with position vectors (3hat(i)- 2 hat(j)+ 4hat(k)),(hat(i) + hat(j) +hat(k)) and (-hat(i)+ 4 hat(j)- 2 hat(k)) respectively are collinear.