Determine unit vector which is perpendicular to both A=2i+j+k and B=i-j+2k?

Question

Determine unit vector which is perpendicular to both A=2i+j+k and B=i-j+2k?

1 Answer

Impact of this question

306133 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-15T15:33:21

We know that cross product of any two vectors yields a vector which is perpendicular to both vectors
$:.$ for two vectors $vecA and vecB$ if $vecC$ is the vector perpendicular to both.
$vecC=vecAxxvecB=$ $[(hati, hatj, hatk), (A_1, A_2,A_3),(B_1, B_2, B_3)]$
$=(A_2B_3−B_2A_3)hati−(A_1B_3−B_1A_3)hatj+(A_1B_2−B_1A_2)hatk$ .
Inserting given vectors we obtain
$vecC=$ $[(hati, hatj, hatk), (2, 1,1),(1, -1, 2)]$
$=(1xx2−(-1)xx1)hati−(2xx2−1xx1)hatj+(2xx(-1)−1xx1)hatk$ .
$=3hati−3hatj−3hatk$ .

Now unit vector in the direction of $vecC$ is $vecC/|vecC|$
$:.|vecC|=sqrt(3^2+(-3)^2+(-3)^2)$
$=sqrt27$
$=3sqrt3$
Therefore desired unit vector is
$1/sqrt3(hati−hatj−hatk)$

Science

Math

Humanities

... and beyond

Determine unit vector which is perpendicular to both A=2i+j+k and B=i-j+2k?

1 Answer

Related questions

Impact of this question