Home
Class 12
MATHS
If points hati+hatj, hati -hatj and p ha...

If points `hati+hatj, hati -hatj and p hati +qhatj+rhatk` are collinear, then

A

`p=1`

B

`r=0`

C

`q in R`

D

`q ne 1`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Points `A(hati + hatj), B(hati -hatj) and C(phati +qhatj + rhatk)` are collinear
Now `vec(AB) = -2hatj and vec(BC) = (p-1)hati + (q-1)hatj + rhatk`
Vectors `vec(AB) and vec(BC)` must be collinear
`rArr p=1, r =0 and q ne 1`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Reasoning Questions)|11 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Comprehension)|9 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Single)|34 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|222 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise All Questions|529 Videos

Similar Questions

Explore conceptually related problems

hati.hatj is

If the points whose position vectors 10hati+3hatj,12hati-5hatj and ahati+11hatj are collinear then a is equal to

Determine whether the three vectors 2hati+3hatj+hatk, hati-2hatj+2hatk and 3hati+hatj+3hatk are coplanar.

Show that the vectors hati+2hatj-3hatk , 2hati-hatj+2hatk and 3hati+hatj-hatk are coplanar.

Show that the points vectors are 2hati+3hatj-5hatk,3hati+hatj-2hatk and 6hati-5hatj+7hatk are collinear.

Prove that points hati+2hatj-3hatk, 2hati-hatj+hatk and 2hati+5hatj-hatk form a triangle in space.

The points with position vectors 60hati+3hatj,40hati-8hatj,ahati-52hatj are collinear iff (A) a=-40 (B) a=40 (C) a=20 (D) none of these

Show that the points whose position vectors 4hati + 5hatj + hatk, -hatj -hatk, 3hati + 9hatj + 4hatk and -4hati + 4hatj + 4hatk are coplanar.