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Question: The angle made by the vector 4\(\widehat{i}\)– 3\(\widehat{j}\)+ 5\(\widehat{k}\) with z-axis is -...

The angle made by the vector 4i^\widehat{i}– 3j^\widehat{j}+ 5k^\widehat{k} with z-axis is -

A

(a)30030^{0}

A

(b)45045^{0}

A

(c)90090^{0}

A

(d)1200120^{0}

Explanation

Solution

(b)

cosq = Az∣A→∣\frac{A_{z}}{|\overset{\rightarrow}{A}|} = 542+32+52\frac{5}{\sqrt{4^{2} + 3^{2} + 5^{2}}} = 552\frac{5}{5\sqrt{2}} = 12\frac{1}{\sqrt{2}}

\ q = π4\frac{\pi}{4}