Answer
(c) $ v\cdot \langle -3,0,0 \rangle $ is equal to zero for all choices of $ v $.
Work Step by Step
Since $ v $ lies in $ yz $-plane, then it will take the form $ \langle 0,a,b \rangle $.
(a) $ v\cdot \langle 0,2,1 \rangle =\langle 0,a,b \rangle\cdot \langle 0,2,1 \rangle=2a+b\neq 0$ for some $ a,b $ .
(b) $ v\cdot k =\langle 0,a,b \rangle\cdot \langle 0,0,1 \rangle=b\neq 0$ for some $ b $.
(c) $ v\cdot \langle -3,0,0 \rangle=-3*0+0*a+0 *b=0$ for all choices of $ v $.
(b) $ v\cdot j =\langle 0,a,b \rangle\cdot \langle 0,1,0 \rangle=a \neq 0$ for some $ a $.
