Question

P is a point on the line joining the points A(0, 5, −2) and B(3, −1, 2). If the x-coordinate of P is 6, then its z-coordinate is ______.

विकल्प

• 10

• 6

• –6

• –10

Answer 1

P is a point on the line joining the points A(0, 5, −2) and B(3, −1, 2). If the x-coordinate of P is 6, then its z-coordinate is 6.

Explanation:

The line through the points (0, 5, −2) and (3, −1, 2) is ${\displaystyle \frac{x}{3-0}=\frac{y-5}{-1-5}=\frac{z+2}{2+2}}$

or, ${\displaystyle \frac{x}{3}=\frac{y-5}{-6}=\frac{z+2}{4}}$

Any point on the line is (3k, −6k + 5, 4k − 2), where k is an arbitrary scalar.

3k = 6

⇒ k = 2

The z-coordinate of the point P will be 4 × 2 − 2 = 6.