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Let vec pa n d vec q be any two orthogo...

Let ` vec pa n d vec q` be any two orthogonal vectors of equal magnitude 4 each. Let ` vec a , vec b ,a n d vec c` be any three vectors of lengths `7sqrt(15)a n d2sqrt(33),` mutually perpendicular to each other. Then find the distance of the vector `( vec adot vec p) vec p+( vec adot vec q) vec q+( vec adot( vec pxx vec q))( vec pxx vec q)+( vec bdot vec p) vec p( vec bdot vec q) vec q+( vec bdot( vec pxx vec q))( vec pxx vec q)+( vec cdot vec p) vec p+( vec cdot vec q) vec q+( vec cdot( vec pxx vec q))( vec pxx vec q)` from the origin.

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