Question

verify:

(-1,2,1) , (1,-2,5) (4, -7,8) and (2,-3,4) are the vertics of parrallelogram.​

Answer 1

Answer:

Step-by-step explanation:

First consider the vertices as A B C and D.

Then, using distance formula find the distance of AB BC CD and AD.

Then you will get two sides equal and the other to sides also equal distance.

Therefore ABCD is a parallelogram.

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

${\boxed{\sf\:{Points\;be\;PQRS}}}$

Hence,

PQ = √{(1 + 1)² + (-2 - 2)² + (5 - 1)²}

PQ = √{(2)² + (-4)² + (4)²}

PQ = √(4 + 16 + 16)

PQ = √20 + 16

PQ = √36

PQ = 6

$\textbf{\underline{Here\;we\;get:-}}$

PQ = 6

Now,

QR = √{(4 - 1)² + (-7 + 2)² + (8 - 5)²}

QR = √{(3)² + (-5)² + (3)²}

QR = √(9 + 25 + 9)

QR = √43

$\textbf{\underline{Here\;we\;get:-}}$

QR = √43

Now,

RS = √{(2 - 4)² + (-3 + 7)² + (4 - 8)²}

RS = √{(-2)² + (4)² + (-4)²}

RS = √(4 + 16 + 16)

RS = √(20 + 16)

RS = √36

RS = 6

$\textbf{\underline{Here\;we\;get:-}}$

RS = 6

Now,

SP = √{(-1 - 2)² + (2 + 3)² + (1 - 4)²}

SP = √{(-3)² + (5)² + (-3)²}

SP = √(9 + 25 + 9)

SP = √43

$\textbf{\underline{Here\;we\;get:-}}$

SP = √43

Therefore,

PQ = RS = 6

QR = SP = √43

Opposite sides of quadrilateral PQRS are equal

Hence,

PQRS is a parallelogram