two vectors - P and Q

[logistic_guy]

Let \(\displaystyle \bold{P} = \langle 2,2,1 \rangle\) and \(\displaystyle \bold{Q} = \langle 1,-2,0 \rangle\). Calculate the following.

(a) \(\displaystyle \bold{P} \cdot \bold{Q}\)

(b) \(\displaystyle \bold{P} \times \bold{Q}\)

(c) \(\displaystyle \text{proj}_{\bold{P}} \bold{Q}\)

 

[logistic_guy]

Let \(\displaystyle \bold{P} = \langle 2,2,1 \rangle\) and \(\displaystyle \bold{Q} = \langle 1,-2,0 \rangle\). Calculate the following.

(a) \(\displaystyle \bold{P} \cdot \bold{Q}\)

(b) \(\displaystyle \bold{P} \times \bold{Q}\)

(c) \(\displaystyle \text{proj}_{\bold{P}} \bold{Q}\)

(a)

\(\displaystyle \bold{P} \cdot \bold{Q} = \langle 2,2,1 \rangle \cdot \langle 1,-2,0 \rangle = (2)(1) + (2)(-2) + (1)(0) = 2 - 4 + 0= -2\)