What is the cosine of the angle between two straight lines having direction ratios proportional to $(1, 2, 2)$ and $(2, - 2, 1)$ ?

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If $l, m, n$ are the direction cosines of a straight line in three-dimensional space, what is the value of $l^{2} + m^{2} + n^{2}$ ?
Which formula gives the shortest distance $d$ between two skew lines $r = a_{1} + λ b_{1}$ and…
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Bag I contains 3 red and 4 black balls, while Bag II contains 5 red and 6 black balls. One bag is chosen at random with equal probability an…
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