[填空题]
Nikola is testing his new autonomous underwater vehicle (AUV) fgou d2 y/2)tk/q(dubb or divi)9eijoss v74tlgxh5; d60z awng and surfacing in the Bavi zw7gex loj)59tds0sh; 64lack Sea.
After submersion in the sea, the AUV begins traveling with a speed of 1.5 $\mathrm{~m} \mathrm{~s}^{-1}$ in the direction $2 \mathbf{i}+\mathbf{j}-2 \mathbf{k}$ , where the unit vector \mathbf{i} is due east, $\mathbf{j}$ is due north and $\mathbf{k}$ is perpendicular to the sea surface. The time is measured in seconds and distances are measured in metres.
1. (1) Find the velocity vector of the AUV.$\mathbf{v}_{\mathrm{d}}=a\mathbf{i}+b \mathbf{j}+c\mathbf{k}$ a = b = c =
(2) Write down the diving speed of the AUV.
Nikola's yacht is at $\mathrm{O}$(0,0,0) . The AUV passes under the yacht at time t=0 and its position vector at this moment is $-30 \mathbf{k}$ . $ms^{-1}$
2. Find the displacement of the AUV relative to the yacht one minute later.
At time t=60 , the AUV turns $90^{\circ}$ in the clockwise direction, maintaining the same horizontal speed, and begins surfacing at $0.75 \mathrm{~m} \mathrm{~s}^{-1}$ .$\mathbf{r}_{\mathrm{d}}=a\mathbf{i}+b \mathbf{j}+c\mathbf{k}$ a = b = c =
3. 1. Find the velocity vector of the AUV at the moment it begins surfacing.$\mathbf{v}_{\mathrm{s}}=a\mathbf{i}+b \mathbf{j}+c\mathbf{k}$ a = b = c =
(2) Hence, write down the displacement of the AUV relative to the yacht at time $t^{\prime} $ seconds, where $t^{\prime}=0 $ is the time at which the AUV begins surfacing.
4. Find the time it takes for the AUV to reach the sea surface from the moment it begins surfacing. seconds
5. Find the distance of the AUV from the yacht when it reaches the sea surface. m
