Question

I need help with question 1

Answer 1

(0, 0, 10)

Step-by-step explanation:

To take the cross product of 3d vectors, you can use the below memorization aid. Starting with the i unit vector, cross out the row and column, then take the determinant of what remains. This becomes the coefficient for the unit vector. Repeat for j and k, alternating signs as you go.

`\left[\begin{array}{ccc}i&j&k\\3&1&0\\2&4&0\end{array}\right] =\left|\begin{array}{cc}1&0\\4&0\end{array}\right| i-\left|\begin{array}{cc}3&0\\2&0\end{array}\right| j+\left|\begin{array}{cc}3&1\\2&4\end{array}\right| k\\\\=(1* 0-0* 4)i-(3* 0-0* 2)j+(3*4-1* 2)k\\=0i-0j+10k`

So V as an ordered triplet is (0, 0, 10), and the magnitude of V is 10 (as found with Pythagorean theorem).