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The direction cosines of the vector \(\vec a = (-2\hat i + \hat j -5 \hat k)\) are?

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NIMCET 2017 Official Paper
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  1. -2, 1, -5
  2. \(\frac 1 3, \frac {-1}6, \frac {-5}6\)
  3. \(\frac 2 {\sqrt {30}},\frac 1 {\sqrt {30}},\frac 5 {\sqrt {30}}\)
  4. \(\frac {-2} {\sqrt {30}},\frac 1 {\sqrt {30}},\frac {-5} {\sqrt {30}}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac {-2} {\sqrt {30}},\frac 1 {\sqrt {30}},\frac {-5} {\sqrt {30}}\)
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Detailed Solution

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Concept:

The direction cosines of the vector is the corresponding coordinate of the vector divided by the length/Magnitude of the vector. 

 

Calculation:

Here, \(\vec a = (-2\hat i + \hat j -5 \hat k)\)

\(\rm \vec |a| = \sqrt{(-2)^2+1^2+(-5)^2}=\sqrt {30}\)

The direction cosines of the given vector = \(\frac {-2} {\sqrt {30}},\frac 1 {\sqrt {30}},\frac {-5} {\sqrt {30}}\)

Hence, option (4) is correct.

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