1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A B C D be the parallelogram whose sides A B and A D are represented by the vectors 2 hat i +4 hat j -5 hat k and hat i +2 hat j +3 hat k respectively. Then, if a is a unit vector parallel to A C, then a is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $A B C D$ be the parallelogram whose sides $A B$ and $A D$ are represented by the vectors $2 \hat{ i }+4 \hat{ j }-5 \hat{ k }$ and $\hat{ i }+2 \hat{ j }+3 \hat{ k }$ respectively. Then, if a is a unit vector parallel to $A C$, then $a$ is equal to

Vector Algebra

Solution:

Let $R_1=2 \hat{i}+4 \hat{j}-5 \hat{k}$
image
and $ R _2 =\hat{ i }+2 \hat{ j }+3 \hat{ k } $
$ \therefore $ R(along AC) $ = R _1+ R _2 $
$ =3 \hat{ i }+6 \hat{ j }-2 \hat{ k } $
$ \therefore $ a (unit vector along A C) $ =\frac{R}{|R|} $
$ =\frac{3 \hat{ i }+6 \hat{j}-2 \hat{ k }}{\sqrt{\hat{9}+3 \hat{6}+1}} $
$=\frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k})$