Question

Given that P = (-7, 16) and Q = (-8, 7), find the component form and magnitude of vector QP .

Let u = <4, 8>, v = <-2, 6>. Find u + v.

Answer 1

a)The component form is

`\vec {QP}=\binom{ - 1}{ - 8}`

b)The magnitude is √65

c) <2,14>

Explanation:

Recall that:

`\vec {QP}=\vec {OP}-\vec{OQ}`

We substitute the position vectors to get:

`\vec {QP}=\binom{ - 8}{7} - \binom { - 7}{15}`

We subtract the corresponding components to obtain:

`\vec {QP}=\binom{ - 8 - - 7}{7 - 15}`

This gives:

`\vec {QP}=\binom{ - 8 + 7}{7 - 15}`

This simplifies to:

`\vec {QP}=\binom{ - 1}{ - 8}`

The magnitude of a vector in the component form:

`\binom{x}{y}`

is

`\sqrt{ {x}^(2) + {y}^(2) }`

This means:

`|\vec {QP}|= \sqrt{ {( - 1)}^(2) + {( - 8)}^(2) }`

This simplifies to:

`|\vec {QP}| = √( 1 + 64 )`

`|\vec {QP}| = √( 65 )`

c) We have the vectors u = <4, 8>, v = <-2, 6>.

We want to find:

u+v

This implies that:

u+v=<4,8>+<-2,6>

We add the corresponding components to get;

u+v=<4+-2,8+6>

This simplifies to:

u+v=<2,14>