Home
Class 12
MATHS
Statement 1: if three points P ,Qa n ...

Statement 1: if three points `P ,Qa n dR` have position vectors ` vec a , vec b ,a n d vec c` , respectively, and `2 vec a+3 vec b-5 vec c=0,` then the points `P ,Q ,a n dR` must be collinear. Statement 2: If for three points `A ,B ,a n dC , vec A B=lambda vec A C ,` then points `A ,B ,a n dC` must be collinear.

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
A
`2veca + 3 vecb-5 vecc=0`
`rArr 3(vecb- veca) = 5(vecc- veca) rArr vec(AB) = (5)/(3) vec(AC)`
Hence, `vec(AB) and vec(AC)` must be parallel since there is a common point A. The points A, B and C must be collinear.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|11 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise MATRIX-MATCH TYPE|3 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|13 Videos

  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|541 Videos