Question

If p = xi + yj + zk, then find |p × k|².

Answer 1

Answer:

|p × k|² = x²+y²

Step-by-step explanation:

To find |p × k|²

we first find |p × k|

since

$\vec p=x\hat i+y\hat j+z\hat k\\\\and\\\\\hat k\\\\(\vec p \:\times\:\hat k) =\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\x&y&z\\0&0&1\end{array}\right|\\\\=y\hat i-x\hat j$

for finding the value of |p × k|

$=\sqrt{y^{2}+x^{2}}$

So

|p × k|² = x²+y²