HOW TO FIND THE PERPENDICULAR DISTANCE BETWEEN TWO SKEW LINES AND PARALLEL LINES

Shortest distance between two parallel lines,perpendicular distance between two parallel lines,shortest distance between two skew lines Cartesian form,shortest distance formula in 3d,distance between two non parallel lines,shortest distance between two parallel lines The Shortest Distance Between Skew Lines

The shortest distance between the lines is the distance which is perpendicular to both the lines given as compared to any other lines that joins these two skew lines.

Vector Form

We shall consider two skew lines  L1 and L2 and  we are to calculate the distance between them. The equations of the given lines are:
The magnitude of this vector
= (169+64+4)=(237)

= (0)(-13)+(-6)(8)+(5)(-2)
= -48 -10
= -58

Taking the absolute value of

Now putting all these values in SD Formula written above , we can have

SD = 58/(237) Units

The Shortest Distance Between Parallel Lines

Consider two parallel lines

Put all these values in the formula given below and the value so calculated is the shortest distance between two Parallel Lines, and if it comes to be negative then take its absolute value as distance can not be negative

Problem 2 : How to find  the shortest distance between two Parallel lines in vector form whose equations are given by

As we know these are parallel line because both these equations are parallel to same vector  -2i +3J+5k.

After solving this determinant and  simplification we get ,

The magnitude of this vector is
2069

Put all these values in the formula given below and the value so calculated is the shortest distance between two Parallel Lines, and if it comes to be negative then take its absolute value as distance can not be negative
SD = √(2069 /38) Units

At Last

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