+91-8076753736[email protected]
logo
logo
-->

Vector Algebra

Question
CBSEENMA12034004
Wired Faculty App

Show that the three points having position vectors
straight a with rightwards arrow on top space minus space 2 straight b with rightwards arrow on top space space plus space space 3 straight c with rightwards arrow on top comma space space minus 2 space straight a with rightwards arrow on top space plus space 3 space straight b with rightwards arrow on top space plus space 2 space straight c with rightwards arrow on top comma space minus 8 space straight a with rightwards arrow on top space plus space 13 space straight b with rightwards arrow on top are collinear whatever be straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top

Solution

Let straight a with rightwards arrow on top space minus space 2 straight b with rightwards arrow on top space plus space 3 space straight c with rightwards arrow on top comma space space space minus 2 space straight a with rightwards arrow on top space plus space 3 space straight b with rightwards arrow on top space plus space 2 space straight c with rightwards arrow on top comma space space minus 8 space straight a with rightwards arrow on top space plus space 13 space straight b with rightwards arrow on top be the position vectors of A, B, C respectively...
AB with rightwards arrow on top space equals space straight P. straight V. space of space straight B space minus space straight P. straight V. space of space straight A space equals space minus 2 straight a with rightwards arrow on top space plus space 3 straight b with rightwards arrow on top plus space 2 space straight c with rightwards arrow on top space minus space straight a with rightwards arrow on top space plus space 2 space straight b with rightwards arrow on top space minus space 3 straight c with rightwards arrow on top space equals space minus 3 space straight a with rightwards arrow on top space plus space 5 space straight b with rightwards arrow on top space minus space straight c with rightwards arrow on top
AC with rightwards arrow on top space equals space straight P. straight V. space of space straight C space minus space straight P. straight V. space of space straight A space equals space minus 8 straight a with rightwards arrow on top space plus space 13 space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top space plus space 2 space straight b with rightwards arrow on top space minus space 3 space straight c with rightwards arrow on top space equals space minus 9 straight a with rightwards arrow on top space plus space 15 space straight b with rightwards arrow on top minus 3 space straight c with rightwards arrow on top
therefore space space space space space AC with rightwards arrow on top space equals space 3 space AB with rightwards arrow on top space space space space space space space rightwards double arrow space space space space AC with rightwards arrow on top space and space AB with rightwards arrow on top space are space parallel space vectors
But A is their common point
∴  point A, B, C are collinear.

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
2 meters north-west

Classify the following measures as scalars and vectors.
40°

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s2

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation