Let v1=(2,-6) and v2=(-4,7) a. compute |v1| and |v2| b. computer the unit vectors in the direction of |v1| and |v2|

In item a, we find the magnitude of each vector, and then, we use this magnitude to find a unit vector in the same direction as the given vectors in item b.

-----------------

Magnitude of a vector:

The magnitude of a vector v = (x,y) is given by:

-----------------

Item a:

v1=(2,-6), the magnitude of v1 is:

v2=(-4,7), the magnitude of v2 is:

-----------------

Item b:

To find the unit vector, in the same direction, each component of the vector is divided by it's magnitude.

v1=(2,-6), magnitude . Thus, the unit vectors in the direction of v1 is:

For v2, same thing:

A similar question is given at link

The magnitude of each vector is the Pythagorean sum of its components.

a. |v1| = √(2² + (-6)²) = √40 = 2√10

|v2| = √((-4)² + 7²) = √65

b. To make each vector into a unit vector, divide each component by the vector's magnitude.

u1 = v1/|v1| = (2/(2√10), -6/(2√10))

u1 = (√10/10, -3√10/10)

u2 = v2/|v2| = (-4/√65, 7/√65)

u2 = (-4√65/65, 7√65/65)

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap