Module 2: Now You Try II

1. Compute the dot product between $x=(-1,2,7)$ and $y=(2,0,-1)$.

Solution:

$x \cdot y = -2+0-7 = -9.$

2. Find all values of $t$ so that $(t,t^2) \cdot (-1,1) = -1.$

Solution:

$(t,t^2) \cdot (-2,1) = t^2-2t = -1.$

This gives the polynomial equation $t^2-2t+1=0$. Factoring gives

$(t-1)^2=0 \Rightarrow t=1.$