A point on a line has coordinates (p + 1, p - 3, √2p) where p is any real number. What are the direction cosines of the line?

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Concept:

If a, b and c are direction ratio’s of a line then direction cosines of the line are given by:

Calculation:

Given: A point on a line has coordinates (p + 1, p - 3, √2p)

⇒ x = p + 1 ⇒ x - 1 = p     ---(1)

⇒ y = p - 3 ⇒ y + 3 = p     ---(2)

⇒ z = √2 × p ⇒   = p   ---(3)

From (1), (2) and (3) we can say that

∴ Direction ratios are: 1, 1, √2

⇒ Direction cosines are: 

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