To solve using parallelogram method, draw the two vectors on the same initial point. (See Fig.1 in the attachment.)

Then, draw another two lines in such a way that a parallelogram is formed. (See Fig.2)

The angle between the two vectors is:

`35^o +75^o=110^o`

Applying the property of a parallelogram --- consecutive angles are supplementary, then the other angle is:

`180^o - 110^o=70^o`

And draw a diagonal starting from the initial position. This represents the resultant vector. (See Fig.3)

To solve for the magnitude of the resultant vector, apply Cosine Law.

`c^2=a^2+b^2-2abcosC`

`R^2=45^2+65^2-2(45)(65)cos(70^o)`

`R^2=4249.18`

`R=65.19 km`

To solve for theta, apply Cosine Law again.

`b^2=a^2+c^2-2ac cosB`

`65^2=45^2+65.19^2-2*45*65.19cos(theta)`

`cos(theta)= (45^2+65.19^2-65^2)/(-2*45*65.19)`

`theta = cos^(-1)((45^2+65.19^2-65^2)/(-2*45*65.19))`

`theta=69.55^o`

Using the East axis as the reference for its direction, then the direction of the resultant vector is:

`theta_f = 69.55^o - 35^o`

`theta_f =34.55^o` (See Fig.4)

Therefore, the final position of the plane is 65.19km away from its starting point, and its direction is 34.55 degree North of East.

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