Question

The unit vector normal to the plane containing vector a = (i - j - k) and vector b = (i + j + k) is

A. (j - k)

B. (-j + k)

C. 1/√2 (-j + k)

D. 1/√2 (-i + k)

Answer 1

Answer is : C. 1/√2 (-j + k)

Given - vector a = (i - j - k) and vector b = (i + j + k)

To find – A unit vector perpendicular to the two given vectors.

Formula to be used -

Tip – A vector perpendicular to two given vectors is their cross product.

The unit vector of any vector ai + bj + ck is given by \(\frac{(a\hat i+b\hat j+c\hat k)}{\sqrt{a^2+b^2+c^2}}\)

Hence,

which the vector perpendicular to the two given vectors.

The required unit vector