Let v = (7, 8). suppose w ∈ double-struck r2 is perpendicular to v, and that w = 7. this determines w up to sign. find one such w

As per the given statement:

Let w ∈ i.e w = (a, b)

then,

by perpendicular to v means;

or

Divide both sides by 7 we get;

                      ......[1]

so, for some values of b.

Using the fact: ||w|| = 7 we get;

substitute the given values, we have;

Squaring both sides we have;

Simplify:

Or

or

Substitute the value of b in [1] we get;

therefore, two such answers of w are;

i think its doubled. let me know

step-by-step explanation: