Question

Find a vector of magnitude √171 which is perpendicular to both the vetor i+2j-3k and 3i-j+2k

Answer 1

Answer:

The required vector is

$u=i-11j-7k$

Explanation:

Let the given vectors are

v = i+2j-3k

w = 3i-j+2k

$v*w=\left[\begin{array}{ccc}i&j&k\\1&2&-3\\3&-1&2\end{array}\right]\\\\v*w= i(4-3)-j(2+9)+k(-1-6)\\\\v*w= i-11j-7k$

v × w = i- 11 j - 7 k

$|v*w| =\sqrt{(1)^{2)}+(-11)^{2}+(-7)^{2}} \\\\|v*w| =\sqrt{171}$

|v × w| = √171

Now let "n" be the unit vector Perpendicular to both v & w, then

n = 1/|v × w| [v × w]

n = 1/√171 [i- 11 j - 7 k]

Let 'u' be the required vector of magnitude √171 and Perpendicular to both v & w, then

u = √171/√171 [i- 11 j - 7 k]

u = i - 11 j - 7 k

$u=i-11j-7k$