Question

Find the distance from the line passing through points P(0,0,0) and Q(9,0,0) to the line passing through points R(3,-2,4) and S(3,-6,-8).

Answer 1

Explanation:

Let the I line be PQ and II line be RS

Direction ratios of PQ = (9,0,0) and direction ratios of RS = (0, -4, -12)

Distance between skew lines

=(a1-a2).(b1xb2)/|b1xb2|

where a1 and a2 are points

Here a1-a2 = (-3,2,-4) taking P and Q as points.

b1 = (9,0,0) and b2 = (0,-4,-12)

Shortest Distance = (a2-a1).(b1xb2)/|b1xb2|

De
`\left[\begin{array}{ccc}-3&2&-4\\9&0&0\\0&-4&-12\end{array}\right]`

Numerator = -9(-24-16)=360

Denominator vector = i(0)-j(-108)+k(-36)

Modulus of vector =\sqrt{108^2+36^2} =36\sqrt{10}

Hence Shortest distance = \sqrt{10}