+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Vector Algebra

Question
CBSEENMA12034001
Wired Faculty App

Prove that if straight u with rightwards arrow on top space equals space straight u subscript 1 space straight i with hat on top space plus space straight u subscript 2 space straight j with hat on top space and space straight v with rightwards arrow on top space equals space straight v subscript 1 space straight i with hat on top space plus space straight v subscript 2 space straight j with hat on top are non-zero vectors, then they are parallel if and only if u2v2 – u2v1 = 0.

Solution

Let straight u with rightwards arrow on top space equals space straight u subscript 1 straight i with hat on top space plus space straight u subscript 2 straight j with hat on top comma space space straight v with rightwards arrow on top space equals space straight v subscript 1 straight i with hat on top space plus space straight v subscript 2 straight j with hat on top be parallel vectors. 
therefore space space space there space exists space straight a space non minus zero space scalar space straight k space such space that space straight u with rightwards arrow on top space equals space straight k space straight v with rightwards arrow on top therefore space space space space straight u subscript 1 straight i with hat on top space plus space straight u subscript 2 straight j with hat on top space equals space straight k left parenthesis straight v straight i with hat on top space plus space straight v subscript 2 straight j with hat on top right parenthesis or space space left parenthesis straight u subscript 1 space space minus space kv subscript 1 right parenthesis space equals space 0 comma space space space straight u subscript 2 space minus kv subscript 2 space equals space 0 therefore space space space space straight k space equals space straight u subscript 1 over straight v subscript 1 comma space space space straight k space equals space straight u subscript 2 over straight v subscript 2 Equating space values space of space straight k comma space we space get comma space space space space space space space space space space space space space space space space space space space space straight u subscript 1 over straight v subscript 1 space equals space straight u subscript 2 over straight v subscript 2 therefore space space space space space space space space straight u subscript 1 straight v subscript 2 space equals space straight u subscript 2 straight v subscript 1 space space space space space space space space space rightwards double arrow space space space space space straight u subscript 1 straight v subscript 2 space minus space straight u subscript 2 space straight v subscript 1 space equals space 0
Similarly, if straight u subscript 1 space straight v subscript 2 space equals space straight u subscript 2 space straight v subscript 1 space space space space rightwards double arrow space space space space space straight u subscript 1 space straight v subscript 2 space minus space straight u subscript 2 space straight v subscript 1 space equals space 0
i.e.,       straight u with rightwards arrow on top comma space space straight v with rightwards arrow on top are parallel
Hence the result.
   

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

Classify the following measures as scalars and vectors.
distance

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation