Find the shortest distance (in units) between the lines 2y= -2x- 4 and -3y=3x-6
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
Step 1. Expressing the first straight line in terms of direction cosines
The given straight line is
The equations in terms of direction cosines be
Step 2. Expressing the second straight line in the symmetrical form
The given straight line is
Let the direction ratios of the above straight line be .
Since the straight line is perpendicular to the normals of both the planes, we have
By cross-multiplication, we get
Hence the direction ratios of the straight line are .
Let us take . Then,
Solving, we get .
Therefore the point on the straight line is .
Hence the equations of the straight line are
Here the direction cosines of the above line are
.
So the line can be rewritten as,
Step 3. Applying distance formula to find the shortest distance between the two given lines
We have found two straight lines
Applying the shortest distance formula between two straight lines, we get the required distance as,
units
units
units [ Expanding along the first row ]
units
units
units
units
units
Answer:
The shortest distance is units.
Formula to find the shortest distance between to skew lines:
Let two skew lines be
where and are direction cosines.
The shortest distance formula is