All categories

2 years ago

Prove that PQ + QR + RS + SP = 0 in the given quadrilateralPQRS

Mathematics

1 answer:

Katarina [22]2 years ago

7 0

Step-by-step explanation:

Using ∆ law of vector addition,

PR→=PQ→+QR→PR→=PQ→+QR→ - (i)

Also,

RP→=RS→+SP→RP→=RS→+SP→ - (ii)

Taking LHS,

=PQ→+QR→+RS→+SP→=PQ→+QR→+RS→+SP→

[Put value of PR→=PQ→+QR→PR→=PQ→+QR→ from equation (i) ]

=(PR→)+RS→+SP→=(PR→)+RS→+SP→

[Put value of RP→=RS→+SP→RP→=RS→+SP→ from equation (ii) ]

=PR→+RP→=PR→+RP→

=PR→−PR→=PR→−PR→

=0=0

RHS

You might be interested in

In a school, only 13 out of 15 student participate in a competition.what is the probability of the student who do not makes it t

Papessa [141]

Answer:

$\frac{2}{15}$

Step-by-step explanation:

Number of students participating in the competition = 13.

Total number of students in the school = 15.

Thus ,

the number of students who did not make to this competition =

Total number of students - number of students participated

= 15-13 = 2.

Now ,

probability of the student who do not makes it to the competition

= fraction of students who did not make to this competition from the total number of students .

= $\frac{2}{15}$ .

4 0

3 years ago

How do you find a vector of length 10 in the direction of vequals=left angle 3 comma negative 2 right angle3,−2?

Kazeer [188]

First we look for the angle of the vector, which will be given by:
tan (x) = (- 2/3)
Clearing x we have:
x = ATAN (-2/3) = - 33.69 degrees.
Which means that the angle is 33.69 degrees measured clockwise from the x axis.
Equivalently the angle is
360-33.69 = 326.31 degrees
326.31 degrees measured counterclockwise from the x axis.
The vector is then:
v = 10 (cos (326.31) i + sin (326.31) j)
answer
v = 10 (cos (326.31) i + sin (326.31) j)

4 0

2 years ago

I need help like RN!!!<br> what are the foci of the ellipse? graph the ellipse. 18x^2+36y^=648

Thepotemich [5.8K]

Hi,

$18x^2+36y^2=648\\

\Rightarrow ( \dfrac{x}{6})^2+( \dfrac{y}{3* \sqrt{2} } )^2=1\\

a=6,\ b=3* \sqrt{2}\\

c= \sqrt{a^2-b^2} = \sqrt{36-18} =3* \sqrt{2}\\

$
Center is (0,0)
Foci are (-3√2,0) and (3√2,0)

7 0

3 years ago

Read 2 more answers

Item 19 The scale on a map is 1 cm:30 mi. The distance on the map between San Francisco, CA, and Chicago, IL, is 61.9 cm. What i

Harlamova29_29 [7]

Answer:

1857 miles.

Step-by-step explanation:

We have been given that the scale on a map is 1 cm:30 mi. The distance on the map between San Francisco, CA, and Chicago, IL, is 61.9 cm. We are asked to find the actual distance between San Francisco and Chicago.

We will use proportions to solve our given problem.

$\frac{\text{Actual distance}}{\text{Map distance}}=\frac{30\text{ miles}}{1\text{ cm}}$