Find the direction cosines of the vector (1, 0, 0).

A. (1, 0, 0) — Direction cosines are the components of the unit vector.

JEE Main · MathematicsEasy

$Find the direction cosines of the vector v = \hat{i} .$

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Correct answer: A — $(1, 0, 0)$

$The vector is v = (1, 0, 0) .$
$The magnitude of the vector is ∣ v ∣ = 1^{2} + 0^{2} + 0^{2} = 1 .$
$The direction cosines are (l, m, n) = (\frac{v _{x}}{∣ v ∣}, \frac{v _{y}}{∣ v ∣}, \frac{v _{z}}{∣ v ∣}) .$
$Calculating gives (\frac{1}{1}, \frac{0}{1}, \frac{0}{1}) = (1, 0, 0) .$
$Hence the answer is (A).$

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