Question

find unit vector perpendicular to vector
A vector=4i-j+3k
B vector=2i+j-2k

Answer 1

Answer:

Find the perpendicular vector using cross product and then find the unit vector along the perpendicular vector

-i + 14j + 6k/√233

Answer 2

We are given that two vectors are

$a = 4i - j + 3k$

$b = - 2i + j - 2k$

Let c is a unit vector which is perpendicular to the given vectors.

$c = a \times b$

We have to find a vector which is perpendicular to both vectors a and b.

Therefore, we find by determinant

$a \times b = | \frac{4. - 1.3}{ - 2.1. - 2} |$

Expand along

$a \times b = i(2 - 3) - j( - 8 + 6) + k(4 - 2)$

$a \times b = - i + 2j + 2k$

$|a \times b| = \sqrt{ {1}^{1} + {2}^{3} + {2}^{2} }$

$|a \times b| = \sqrt{1 + 4 + 4}$

$|a \times b| = \sqrt{9} = 3$

The unit vector perpendicular to both vectors a and b is given by

$c = \frac{c}{ |c| }$

The unit vector,

$c = \frac{ - i + 2j + 22}{3}$

Hence, the unit vector c is perpendicular to the vectors a and b is given by

$c = - \frac{1}{3} i - \frac{2}{3} j + \frac{2}{3} k$