Question

Find the scalar components of a unit vector which is perpendicular to the vectors i+2j-k and 3i-j+2k

Answer 1

Answer:

$\frac{3 \hat i}{ \sqrt{83} } - \frac{5\hat j}{ \sqrt{83} } - \frac{7 \hat k}{ \sqrt{83} } \\ \:$

Step-by-step explanation:

Let the vector perpendicular to the vectors i+2j-k and 3i-j+2k is

$x \hat i + y\hat i + z\hat k$

If two vectors are perpendicular than their dot product is zero.

Find dot product

$x + 2y - z = 0 \\ 3x - y + 2z = 0$

Now solve these two homogeneous equations

$\frac{x}{4 - 1} = \frac{ - y}{2 + 3} = \frac{z}{ - 1 - 6} \\ \\ \frac{x}{3} = \frac{ y}{ - 5} = \frac{z}{ - 7} = m \\ \\ x = 3m \\ y = - 5m \\ z = - 7m$

Hence the vector is

$3 \hat i - 5\hat i - 7\hat k$

Now to find the unit vector; find the magnitude

$\sqrt{9 + 25 + 49} \\ \\ = \sqrt{83}$

Unit vector which is perpendicular to the given vectors

$\frac{3 \hat i}{ \sqrt{83} } - \frac{5\hat j}{ \sqrt{83} } - \frac{7 \hat k}{ \sqrt{83} }$

Hope it helps you.

Answer 2

Answer:

Step-by-step explanation:

hope it will help u