Home
Class 12
MATHS
If the position vectors of the points A,...

If the position vectors of the points A, B, C are `2hat(i) + hat(j) - hat(k), 3hat(i) - 2hat(j) + hat(k)` and `hat(i) + 4hat(j) - 3hat(k)` respectively, then prove that A, B, C are collinear.

Text Solution

Verified by Experts

The correct Answer is:
Since, B is common point between `vec(AB)` and `vec(BC)` Therefore, A,B and C are collinear.
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    ARIHANT PRAKASHAN|Exercise TOPIC -1 (PRACTICE QUESTIONS) (4 MARK QUESTIONS) |12 Videos

  • VECTORS

    ARIHANT PRAKASHAN|Exercise TOPIC TEST 1|16 Videos

  • THREE DIMENSIONAL GEOMETRY

    ARIHANT PRAKASHAN|Exercise CHAPTER TEST|24 Videos

  • VERY SIMILAR TEST 1

    ARIHANT PRAKASHAN|Exercise Section C |10 Videos

Similar Questions

Explore conceptually related problems

The position vectors of the point A,B,C and D are 4hat(i)+3hat(j)-hat(k),5hat(i)+2hat(j)+2hat(k),2hat(i)-2hat(j)-3hat(k) and 4hat(i)-4hat(j)+3hat(k) , respectively. Show that vec(AB) and vec(CD) are parallel.

Show that the vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

Show that the following vectors are coplanar. hat(i) - 2hat(j) + 2hat(k), 3hat(i) + 4hat(j) + 5hat(k), -2hat(i) + 4hat(j) - 4hat(k)

Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and -4 hat(i) + 3 hat(j) - hat(k) are collinear.

Show that the following vectors are coplanar. hat(i) + 2hat(j) + 3hat(k), -2hat(i) - 4hat(j) + 5hat(k), 3hat(i) + 6hat(j) + hat(k)