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

Vector Algebra

Question
CBSEENMA12034230
Wired Faculty App

Prove that the points A, B and C with position vectors straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top, respectively are collinear if and only if straight b with rightwards arrow on top space cross times space straight c with rightwards arrow on top space plus space straight c with rightwards arrow on top space cross times space straight a with rightwards arrow on top space plus space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space 0 with rightwards arrow on top.

Solution
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 are position vectors of A, B, C respectively.
therefore space space space BC with rightwards arrow on top space equals straight P. straight V. space of space straight C space minus space straight P. straight V. space of thin space straight B space equals space straight c with rightwards arrow on top space minus space straight b with rightwards arrow on top
and CA with rightwards arrow on top space equals space straight P. straight V. space of space straight A space minus space straight P. straight V. space of space straight C space equals space straight a with rightwards arrow on top space minus space straight c with rightwards arrow on top
Points A, B, C are collinear.
                  iff    BC with rightwards arrow on top space cross times space CA with rightwards arrow on top space equals space 0
 i.e.,           iff  left parenthesis straight c with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis space cross times space left parenthesis straight a with rightwards arrow on top space minus straight c with rightwards arrow on top right parenthesis space equals space 0
i.e.,            iff straight c with rightwards arrow on top cross times straight a with rightwards arrow on top space minus space straight c with rightwards arrow on top cross times space straight c with rightwards arrow on top minus straight b with rightwards arrow on top cross times straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space cross times space straight c with rightwards arrow on top space equals space 0 with rightwards arrow on top
i.e.,           iff straight c with rightwards arrow on top cross times straight a with rightwards arrow on top space minus space 0 with rightwards arrow on top space plus straight a with rightwards arrow on top space cross times straight b with rightwards arrow on top space plus space straight b with rightwards arrow on top space cross times space straight c with rightwards arrow on top space space space space space space space space space space space open square brackets because space space straight c with rightwards arrow on top space cross times space straight c with rightwards arrow on top space equals space 0 comma space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space minus straight b with rightwards arrow on top space cross times space straight a with rightwards arrow on top close square brackets
i.e.,           iff straight a with rightwards arrow on top cross times straight b with rightwards arrow on top plus straight b with rightwards arrow on top cross times straight c with rightwards arrow on top plus straight c with rightwards arrow on top cross times straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
(i) 5 seconds
(ii) 1000 cm3
(iii) 10 Newton
(iv) 30 km hr
(v) 10 g/cm3
(vi) 20 m/s towards north

Classify the following measures as scalars and vectors.
10 kg

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

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation