+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Vector Algebra

Question
CBSEENMA12034179
Wired Faculty App

Find a unit vector perpendicular to vectors
3 straight i with hat on top space plus space 2 straight j with hat on top space minus space straight k with hat on top comma space space 2 straight i with hat on top space plus straight j with hat on top space plus 3 straight k with hat on top

Solution

Let straight a with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space minus space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space plus space 3 space straight k with hat on top
therefore space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 3 2 cell negative 1 end cell row 2 1 3 end table close vertical bar space equals straight i with hat on top space open vertical bar table row 2 cell negative 1 end cell row 1 3 end table close vertical bar space minus straight j with hat on top space open vertical bar table row 3 cell negative 1 end cell row 2 2 end table close vertical bar space plus space straight k with hat on top space open vertical bar table row 3 2 row 2 1 end table close vertical bar space space space space space space space space space space space space space space space space space space space equals space left parenthesis 6 plus 1 right parenthesis space straight i with hat on top space minus left parenthesis 9 plus 2 right parenthesis space straight j with hat on top space plus space left parenthesis 3 minus 4 right parenthesis space straight k with hat on top therefore space space space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space 7 space straight i with hat on top space minus space 11 space straight j with hat on top space minus space straight k with hat on top therefore space space space open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals space square root of 49 plus 121 plus 1 end root space equals space square root of 171 therefore space space space space unit space vector space perp. space to space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space equals plus-or-minus fraction numerator straight a with rightwards arrow on top cross times straight b with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar end fraction equals space plus-or-minus space fraction numerator 1 over denominator square root of 171 end fraction left parenthesis 7 space straight i with hat on top space minus space 11 space straight j with hat on top space minus space straight k with hat on top right parenthesis space

Some More Questions From Vector Algebra Chapter

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