[填空题]
Emily starts flying her drone from the b(ych11 ll-jek0ra ;b6f jz-nroof of a residential buwyje1s ra-syi3r e+ 8f9 g-e8zilding. The displacement of the drone at time t seconds is given by the vect 8g -frjw+e1i yas3-rez 98esyor equation
$\mathbf{r}_{\mathrm{d}}=\left(\begin{array}{c}
0 \\
0 \\
42
\end{array}\right)+t\left(\begin{array}{c}
4 \\
6 \\
0.4
\end{array}\right), \quad t \geq 0 .$
where distances are measured in metres.
1. Find the position vector of Emily's drone one minute after takeoff.
Frank starts flying his quadcopter (a type of drone) from a tennis court. The displacement of the quadcopter at time s seconds is given by the vector equation
$\mathbf{r}_{\mathrm{q}}=\left(\begin{array}{c}
-420 \\
-360 \\
0
\end{array}\right)+s\left(\begin{array}{c}
10 \\
12 \\
1
\end{array}\right), \quad s \geq 0 .$
where distances are are also measured in metres.$\left(\begin{array}{c}
a \\
b \\
c
\end{array}\right)$ a = b = c =
2. Find the distance between Emily and Frank. ≈ m
3. Determine if the two drone flight paths intersect, and if so, write down the point of intersection.
Emily's drone and Frank's quadcopter started flying at the same time.$\left(\begin{array}{c}
a \\
b \\
c
\end{array}\right)$ a = b = c =
4. State whether the two drones actually collide. Justify your answer.
5. (1) Find the time when Emily's drone is closest to Frank's quadcopter. $t_{min}$ ≈ seconds
(2.)Calculate the minimum distance between the two drones. $d_{min}$ ≈ m
