A

1003188703

Level: 
A
Given points \( A=[-4,1,4] \) and \( B=[4,-3,0] \), determine which of the following parametric equations do not define the line segment \( AB \).
$\begin{aligned} AB\colon x&=-4+8t, \\ y&=1+4t, \\ z&=4-4t,\ t\in[0,1] \end{aligned}$
$\begin{aligned} AB\colon x&=-4+8t, \\ y&=1-4t, \\ z&=4-4t,\ t\in[0,1] \end{aligned}$
$\begin{aligned} AB\colon x&=4+8t, \\ y&=-3-4t, \\ z&=-4t,\ t\in[-1,0] \end{aligned}$
$\begin{aligned} AB\colon x&=-4+2t, \\ y&=1-t, \\ z&=4-t,\ t\in[0,4] \end{aligned}$

1003188702

Level: 
A
We are given points \( A=[-2,3,0] \), \( B=[6,1,6] \) and \( C=[1,0,4] \). Find the parametric equations of a line \( p \) that passes through the point \( C \) and through the midpoint of the line segment \( AB \).
$\begin{aligned} p\colon x&=1+t, \\ y&=2t, \\ z&=4-t,\ t\in\mathbb{R} \end{aligned}$
$\begin{aligned} p\colon x&=1+2t, \\ y&=-t, \\ z&=4-t,\ t\in\mathbb{R} \end{aligned}$
$\begin{aligned} p\colon x&=1-t, \\ y&=2t, \\ z&=4+t,\ t\in\mathbb{R} \end{aligned}$
$\begin{aligned} p\colon x&=1+2t, \\ y&=t, \\ z&=4+t,\ t\in\mathbb{R} \end{aligned}$

1003164406

Level: 
A
Determine whether any of the lines \( p \), \( q \) or \( r \) defined by the parametric equations given below passes through the coordinate origin. \begin{align*} p\colon x&=-2+4t, & q\colon x&=-5-5s, & r\colon x&=3-6u, \\ y&=1-2t, & y&=2-2s, & y&=-\frac12+u, \\ z&=-3+3t,\ t\in\mathbb R & z&=5+5s,\ s\in \mathbb R & z&=2-4u,\ u\in \mathbb R \end{align*}
Yes, it's the straight line \( r \).
Yes, it's the straight line \( p \).
Yes, it's the straight line \( q \).
None of the lines passes through the coordinate origin.

1003164405

Level: 
A
Determine whether the line \( p \) defined by parametric equations: \begin{align*} x&=-2+2t, \\ y&=1+3t, \\ z&=-3+3t,\ t\in\mathbb{R} \end{align*} intersects any of the coordinate axis.
Yes, it intersects the \( y \)-axis.
Yes, it intersects the \( x \)-axis.
Yes, it intersects the \( z \)-axis.
It intersects no coordinate axis.

1003164404

Level: 
A
Let a straight line \( p \) be defined by parametric equations: \begin{align*} x&=3+t, \\ y&=2-t, \\ z&=4,\ t\in\mathbb{R}. \end{align*} Find the coordinates of the intersection point \( M \) of the line \( p \) with the \( xy \)-coordinate plane.
There is no such point \( M \).
\( M=[0,0,4] \)
\( M=[-3,2,0] \)
\( M=[1,-1,0] \)

1003164403

Level: 
A
Let a straight line $p$ be defined by parametric equations: \begin{align*} x&=-1+t, \\ y&=2+3t, \\ z&=5-t,\ t\in\mathbb{R}. \end{align*} Find the coordinates of the intersection point \( M \) of the line \( p \) with the \( yz \)-coordinate plane.
\( M=[0,5,4] \)
\( M=[-1,0,0] \)
\( M=[0,3,-1] \)
\( M=[1,0,0] \)

1003164402

Level: 
A
Let a straight line \( p \) be defined by parametric equations: \begin{align*} x&=-1+2t, \\ y&=2+t, \\ z&=5-t,\ t\in\mathbb{R}. \end{align*} Find the coordinates of the intersection point \( M \) of the line \( p \) with the \( xz \)-coordinate plane.
\( M=[-5,0,7] \)
\( M=[0,2,0] \)
\( M=[-1,0,5] \)
\( M=[2,0,-1] \)

1003164401

Level: 
A
Let a straight line \( p \) be defined by parametric equations: \begin{align*} x&=-1+2t, \\ y&=2+t, \\ z&=5-t,\ t\in\mathbb{R}. \end{align*} Find the coordinates of the intersection point \( M \) of the line \( p \) with the \( xy \)-coordinate plane.
\( M=[9,7,0] \)
\( M=[0,0,5] \)
\( M=[-1,2,0] \)
\( M=[0,0,-1] \)