Find the unit vector perpendicular to the plane
` vec r.(2 hat i+ hat j+2 hat k)=5.`

Find a unit vector perpendicular to both the vectors 2 hat (i) - 3 hat (j) + 6 hat (k) and 3 hat (j) - 4 hat (k) . Also find the sine of the angle between the given vectors .

Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

Find the unit vector in the direction of the vector vec a= hat i+ hat j+ 2 hat k .

Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

In each of the following find a unit a vector perpendicular to both vec (a) and vec (b) vec(a) = 2 hat (i) + hat (j) and vec (b) = - hat (i) + hat (k)

In each of the following find a unit a vector perpendicular to both vec (a) and vec (b) vec(a) = 2 hat (i) - 2 hat (j) + hat (k) and vec (b) = hat (i) + 2 hat (j) - 2 hat (k)

In each of the following find a unit a vector perpendicular to both vec (a) and vec (b) vec(A) = hat (i) + hat (j) and vec (b) = - hat (i) + hat (k)

Given two vectors vec a=- hat i+2 hat j+2 hat ka n d vec b=-2 hat i+ hat j+2 hat kdot Column I, Column II A vector coplanar with vec aa n d vec b , p. -3 hat i+3 hat j+4 hat k A vector which is perpendicular to both vec aa n d vec b , q. 2 hat i-2 hat j+3 hat k A vector which is equally inclined to vec aa n d vec b , r. hat i+ hat j A vector which forms a triangle with vec aa n d vec b , s. hat i- hat j+5 hat k

If vec a= hat i+hat j- hat k, vec b= -hat i+2 hat j+ hat k and vec c = - hat i+2 hat j- hatk , then show that the unit vector perpendicular to vec a+ vec b and vec b+ vec c is hat k .

Find a unit vector perpendicular to each of the vectors ( vec a+ vec b) and ( vec a- vec b) , where vec a= hat i+ hat j+ hat k , vec b= hat i+2 hat j+3 hat k .