Question

If vector u has its initial point at (-7, 3) and its terminal point at (5, -6), u = i + j.

If v = -11i + 3j, 2u − v = i + j.

Answer 1

The vector expressions are:

• $u = (-2 , -3 )$

• $v = (92,-51)$

• $2u - v = (-2,-3)$

What are vectors?

Vectors are objects that have both magnitudes and directions.

The expressions are illustrations of vectors, and the given parameters are:

• Initial point: i = (-7,3)
• Terminal point: j = (5,-6)

Also, we have:

u = i + j.

u = i + j means that:

$u = (5,-6) + (-7,3)$

$u = (5+ (-7) , -6 + 3 )$

$u = (5-7 , -6 + 3 )$

$u = (-2 , -3 )$

Also, we have:

v = -11i + 3j

This becomes

$v = -11 \times (-7,3) + 3 \times (5,-6)$

$v = (77,-33) + (15,-18)$

Rewrite as:

$v = (77+ 15,-33-18)$

$v = (92,-51)$

Also, we have:

2u − v = i + j

and

u = i + j

Substitute i + j for u

$2u - v = u$

Substitute (-2, -3) for u

$2u - v = (-2,-3)$

Read more about vector expressions at:

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