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For p gt 0 vector vecv (2) = 2 hati + (...

For `p gt 0` vector` vecv _(2) = 2 hati + (p + 1 ) hatj ` is obtained by rotating the vector`vec v _(1) = sqrt3 p hati + hatj` by an angle `theta` about origin in counter clockwise direction. If `tan theta = (( alpha sqrt3 - 2)/( 4 sqrt3 + 3)),` then the value of `alpha` is equal to _____________

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