Question

Find the unit vector perpendicular to the plane of a =2i+j-k and b=-i-j+2k

Answer 1

Given: Two vectors: a =2i+j-k and b=-i-j+2k

To find: The unit vector perpendicular to both.

Solution:

• Let c be the vector which is perpendicular to both the given vectors a and b.

• So c = a x b ..........(using cross product)

               c = $\left[\begin{array}{ccc}i&j&k\\2&1&-1\\-1&-1&2\end{array}\right]$

               c = i(2+1) - j(4-1) + k(-2+1)

               c = 3i -3j -k

• So the unit vector of c will be:

               c(cap) = c(vector) / mod(c)

                          = 3i -3j -k / $\sqrt{3^2 + 3^2 + (-1)^2}$

               c(cap) = 3i -3j -k / √19

Answer:

              So, the unit vector perpendicular to both is 3i -3j -k / √19