Question

29.
the lines x + a= 2y=-12z andx = y + 2a
y = 6
Find the length and equation of the line of shortest distance between the lines
3x - 9y + 5z = 0 = x + y - z and 6x + 8y + 32-13 = 0 = x + 2y + z-3.​

Answer 1

Answer:

the answer is 23xy

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Answer 2

Answer:

ok

Step-by-step explanation:

Given lines are

x+1=2y=−12z and x=y+2=6z−6

⇒

1

x−(−1)

=

1/2

y−0

=

−1/12

z−0

and

1

x−0

=

1

y−(−2)

=

1/6

z−1

these lines may be written in vector form as

We know that the shortest distance between

is given

$$\vec{b_1} \times \vec{b_2} = \begin{vmatrix}

\hat{i} & \hat{j}& \hat{k}\\

1 & 1/2& -1/2\\

1& 1& 1/6

\end{vmatrix} = \left ( \dfrac{1}{12} + \dfrac{1}{12} \right )\hat{i} - \left ( \dfrac{1}{6} + \dfrac{1}{12} \right )\hat{j} + \left ( 1 - \dfrac{1}{2} \right )\hat{k}$$

= 2 units