Question

Find the shortest distance between the lines x−3/1 = y−5/−2 ​= z−7/1 and x+1/ 7 = y+1/−6 = z+1/1

A. 2 (sqrt. of 21)
B. 3 (sqrt. of 21)
​C. 2(sqrt. of 29)
D. 3(sqrt. of 21)

Answer 1

The shortest distance between the given lines is 3(sqrt. of 21) (B).

Step-by-step explanation:

To find the shortest distance between two lines, we can use the formula for the distance between two parallel lines. The formula is given by the absolute value of the difference between the constant terms of the two lines divided by the square root of the sum of the squares of the coefficients.

In this case, the distance is |(-7/1) - (-1/1)| / √((-2)^2 + (1/7)^2 + (1)^2), which simplifies to 6/(√(1/4 + 1/49 + 1)). By rationalizing the denominator, we can express the distance as 6(√(49/44)) / (7/2), which simplifies to 3(√21).

So the answer is B.