+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Vector Algebra

Question
CBSEENMA12034002
Wired Faculty App

Find the condition that the vectors straight a with rightwards arrow on top space equals space straight k space straight i with hat on top space plus space 3 space straight j with hat on top space and space straight b with rightwards arrow on top space equals space 4 space straight i with hat on top space plus space straight k space straight j with hat on top comma space space left parenthesis straight k space not equal to space 0 right parenthesis are parallel.

Solution

Here,   straight a with rightwards arrow on top space equals space straight k straight i with hat on top space plus space 3 straight j with hat on top comma space space straight b with rightwards arrow on top space equals space 4 straight i with hat on top space plus space space straight k straight j with hat on top
Let straight a with rightwards arrow on top space and space straight b with rightwards arrow on top   be parallel..
  therefore space space   there exists a non-zero scalar straight lambda such that
               straight a with rightwards arrow on top space equals space straight lambda straight b with rightwards arrow on top
therefore space space straight k space straight i with hat on top space plus space 3 space straight j with hat on top space equals space 4 space straight lambda space straight i with hat on top space plus space straight lambda space straight k space straight j with hat on top therefore space space space left parenthesis straight k space minus space 4 space straight lambda right parenthesis space straight i with hat on top space plus space left parenthesis 3 space minus space straight k space straight lambda right parenthesis space straight j with hat on top space equals space 0 with rightwards arrow on top rightwards double arrow space space space space straight k space minus space 4 space straight lambda space equals space 0 comma space space space space 3 space space minus space straight k space straight lambda space equals space 0 rightwards double arrow space space space space space space space space space space space space space straight lambda space equals straight k over 4 comma space space space space straight lambda space equals space 3 over straight k
Equating values of straight lambda comma we get,
                      straight k over 4 space equals space 3 over straight k space space space or space space space straight k squared space equals space 4 space cross times space 3 space equals space 12
which is required condition. 
             

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

Classify the following measures as scalars and vectors.
force

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation