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Find a vector  \(\vec a\) of magnitude 5√ 2, making an angle of π/4 with x - axis π/2 with y - axis and an acute angle θ with z - axis.

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Let the angles made by vector be α, β, θ and the magnitude be m.

Given that \(\alpha=\cfrac{\pi}4,\) \(\beta = \cfrac{\pi}2\) and m = 5√2. We have to figure out the vector.

Since cos2α + cos2β + cos2θ = 1, we get

Since θ is acute, \(cos\theta=\cfrac{1}{\sqrt2}\)

Any vector, if it’s magnitude and direction cosines are given can be written as

 So, the required vector is

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