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dusya [7]
2 years ago
13

Define the points ​P(negative 4−4​,negative 2−2​) and ​Q(33​,negative 4−4​). Carry out the following calculation. Find two vecto

rs parallel to ModifyingAbove QP with right arrowQP with length 22.
Mathematics
1 answer:
slega [8]2 years ago
8 0

Answer:

The required vectors are u= and v=.

Step-by-step explanation:

Given information: P(-4,-2) and Q(3,-4).

We need to find the two vectors parallel to \overrightarrow {QP} with length 2.

If A(x_1,y_1) and B(x_2,y_2), then

\overrightarrow {AB}=

|\overrightarrow {AB}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using the above formula we get

vector QP is,

\overrightarrow {QP}==

Magnitude of vertor QP is,

|\overrightarrow {QP}|=\sqrt{(-4-3)^2+(-2-(-4))^2}

|\overrightarrow {QP}|=\sqrt{(-7)^2+(2)^2}

|\overrightarrow {QP}|=\sqrt{49+4}

|\overrightarrow {QP}|=\sqrt{53}

Using vector is

\widehat {QP}=\frac{\overline {QP}}{|\overline {QP}|}

\widehat {QP}=\frac{1}{\sqrt{53}}

w=\widehat {QP}=\frac{1}{\sqrt{53}}

Multiply vector w by 2 to get a parallel vector parallel of QP in same direction.

u=2w=

Multiply vector w by -2 to get a parallel vector parallel of QP in opposite direction.

v=-2w=

Therefore the required vectors are u= and v=.

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