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Show that the sum of the length of projections of piqjrkpi^+qj^+rk^ on the coordinate axes, where p = 2, q = 3 and r = 4 is 9. - Mathematics and Statistics

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Sum

Show that the sum of the length of projections of `"p"hat"i" + "q"hat"j" + "r"hat"k"` on the coordinate axes, where p = 2, q = 3 and r = 4 is 9.

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Solution

Let `bar"a" = "p"hat"i" + "q"hat"j" + "r"hat"k"`

Projection of `bar"a"` on X-axis

`= (bar"a".hat"i")/|hat"i"| = (("p"hat"i" + "q"hat"i" + "r"hat"k").hat"i")/1` = p = 2

Similarly, projections of `bar"a"` on Y- and Z-axes are 3 and 4 respectively.

∴ sum of these projections = 2 + 3 + 4 = 9.

Concept: Vector Product of Vectors (Cross)
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