Q .13. - Calculus

Question

Find the points where the line 

$x=t+2, y=2 t-5, z=-4 t-7$

intersects each of the coordinate planes 

Step-by-Step Solution

Answer

$\text{ The required answer is }(0,-9,1)\left(\frac{9}{2},0,-17\right)\left(\frac{1}{4},\frac{-17}{2},0\right)\text{. }$

Step 1:Given information

The line is 

$x=t+2, y=2 t-5, z=-4 t-7$

Step 2:Calculation

$\text{ Consider the line }\mathcal{L}\text{ determined by the equations }x=t+2,y=2t-5,z=-4t-7\text{. }$

$\text{ Take the line }\mathcal{L}\text{ equation. }$

$x=t+2, y=2 t-5, z=-4 t-7$

Then,

$r\left(t\right)=(t+2,2 t-5,-4 t-7)$

 When the line intersect in  yz-plane the value of $x=0$

$\text{ Now substitute }x=0\text{ in }x=t+2\text{. }$

$0=t+2$

$\Rightarrow t=-2$

$\text{ Substitute }t=-2\text{ in }r\left(t\right)=(t+2,2t-5,-4t-7)\text{. }$

$r(-2)=(0,2·-2-5,-4·-2-7)$

$r(-2)=(0,-9,1)$

$\text{ Thus the point in }yz\text{-plane is }(0,-9,1)$