The points A(5, -1, 1), B(7, -4, 7), C(1

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

The points A(5, -1, 1), B(7, -4, 7), C(1, -6, 10) and D(-1, -3, 4) are vertices of a

Options:

trapezium

rectangle

rhombus

square

Correct Answer:

rhombus

Explanation:

It can easily be seen thet AB = BC = CD = DA = 7.

So, ABCD is a rhombus. Also, $\vec{AB}, \vec{BC}≠ 0.$

So, Ab is not perpendicular to BC. Therefore, ABCD is not a square.

But, $\vec{AC}. \vec{BD}= 0.$

Hence, ABCD is a rhombus.