+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Vector Algebra

Question
CBSEENMA12034066
Wired Faculty App

Let straight a with rightwards arrow on top space equals space 5 straight i with hat on top space minus space straight j with hat on top space plus space 7 straight k with hat on top and straight b with rightwards arrow on top space equals straight i with hat on top minus straight j with hat on top plus straight lambda straight k with hat on top. Find straight lambda such that straight a with rightwards arrow on top plus straight b with rightwards arrow on top and straight a with rightwards arrow on top minus straight b with rightwards arrow on top are orthogonal .

Solution

   straight a with rightwards arrow on top space equals space 5 straight i with hat on top minus straight j with hat on top plus 7 straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space straight i with hat on top minus straight j with hat on top plus straight lambda straight k with hat on top
therefore space space straight a with rightwards arrow on top plus straight b with rightwards arrow on top space equals 6 space straight i with hat on top space minus 2 space straight j with hat on top space plus left parenthesis straight lambda plus 7 right parenthesis space straight k with hat on top comma space space straight a with rightwards arrow on top minus straight b with rightwards arrow on top space equals 4 space straight i with hat on top plus left parenthesis 7 minus straight lambda right parenthesis space straight k with hat on top
Since straight a with rightwards arrow on top plus straight b with rightwards arrow on top space and space straight a with rightwards arrow on top space minus straight b with rightwards arrow on top are orthogonal
therefore space space space space left parenthesis straight a with rightwards arrow on top space plus straight b with rightwards arrow on top right parenthesis. space left parenthesis straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top right parenthesis space equals space 0 therefore space space space space left parenthesis 6 right parenthesis left parenthesis 4 right parenthesis plus left parenthesis negative 2 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis 7 plus straight lambda right parenthesis space left parenthesis 7 minus straight lambda right parenthesis space equals space 0 therefore space space space 24 plus 49 minus straight lambda squared space equals space 0 space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space straight lambda squared space equals space 73 therefore space space space space space space space space straight lambda space equals plus-or-minus square root of 73

Some More Questions From Vector Algebra Chapter

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