Answer :

Given that,

Magnitude of vector = 14

Also, direction ratios = 2 : 3 : -6

Also can be defined as,

Know that, the direction cosines of a vector are the cosines of the angles between the vector and the three coordinate axes.

∴, the direction cosines l, m and n are

[∵ ]

[∵ ]

[∵ ]

And we know that,

l^{2} + m^{2} + n^{2} = 1

⇒ 49k^{2} = 196

⇒ k^{2} = 4

⇒ k = ±√4

⇒ k = ±2

Since, makes an acute angle with x-axis, then k will be positive.

⇒ k = 2

The direction cosines are

The components of can be found out by,

Thus, the direction cosines (l, m, n) are ; and the components of are .

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