# Two non collinear position vectors #veca & vecb# are inclined at an angle #(2pi)/3#,where #|veca|=3 & |vecb|=4 #. A point P moves so that #vec(OP)=(e^t+e^-t)veca +(e^t-e^-t)vecb#. The least distance of P from origin O is #sqrt2sqrt(sqrtp-q)# then p+q =?

##### 2 Answers

#### Explanation:

Now,

with real solution at

Here

Choosing x-axis in the direction of the vector

Now, the vector in the addition for the vector

multiples of

respectively.

And so, the angle in between is

Now,

Beyond this, I follow the previous answer, with due compliments

to Cesareo.

Of course, I can add that vector

The angle ie what this makes with vector

A graphical depiction could enhance the merits of this nonpareil

problem.

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