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

Vector Algebra

Question
CBSEENMA12034105
Wired Faculty App

Find λ when the scalar projection of straight a with rightwards arrow on top space equals space straight lambda straight i with hat on top space plus space straight j with hat on top space plus space 4 straight k with hat on top space space and space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 6 straight j with hat on top space plus space 3 straight k with hat on top space is space 4 space units.

Solution

Here   straight a with rightwards arrow on top space equals space straight lambda space straight i with hat on top space plus space straight j with hat on top space plus space 4 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 6 space straight j with hat on top space plus space 3 space straight k with hat on top
therefore space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space square root of 4 plus 36 plus 9 end root equals space square root of 49 space equals space 7
                straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space left parenthesis straight lambda right parenthesis space left parenthesis 2 right parenthesis space plus space left parenthesis 1 right parenthesis thin space left parenthesis 6 right parenthesis space plus space left parenthesis 4 right parenthesis thin space left parenthesis 3 right parenthesis space equals space 2 space straight lambda space plus 6 plus 12 space equals space 2 straight lambda plus 18
Scalar projection of straight a with rightwards arrow on top space and space straight b with rightwards arrow on top = fraction numerator straight a with rightwards arrow on top. space straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar end fraction
 therefore space space space 4 space equals space fraction numerator 2 space straight lambda space plus space 18 over denominator 7 end fraction space space space space space rightwards double arrow space space space space 28 space equals space 2 straight lambda plus 18 space space space space rightwards double arrow space space space 2 space straight lambda space equals space 10 therefore space space space space space straight lambda space equals space 5

Some More Questions From Vector Algebra Chapter

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

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