Question 3

If a line has the direction ratios −18, 12, −4, then what are its direction cosines?

Answer

If a line has direction ratios of −18, 12, and −4, then its direction cosines are

\begin{align} \frac{-18}{\sqrt {(-18)^2 + (12)^2 + (-4)^2}},\frac{12}{\sqrt {(-18)^2 + (12)^2 + (-4)^2}},\frac{-4}{\sqrt {(-18)^2 + (12)^2 + (-4)^2}}\end{align}

\begin{align} i.e., \frac{-18}{22},\frac{12}{22},\frac{-4}{22}\end{align}

\begin{align} \frac{-9}{11},\frac{6}{11},\frac{-2}{11}\end{align}

Thus, the direction cosines are

\begin{align} \frac{-9}{11},\frac{6}{11} and \frac{-2}{11}\end{align}

Popular Questions of Class 12 Mathematics

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(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.
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(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
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(iv) Relation R in the set Z of all integers defined as
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(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y}
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In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

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If a line has the direction ratios −18, 12, −4, then what are its direction cosines?

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