Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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 ⇒
From (1), (2) and (3) we can say that
∴ Direction ratios are: 1, 1, √2
⇒ Direction cosines are:
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