Area of a rectangle having vertices A- B- C- and D with position vectors -1-2-4 k- -1-2-4 k- -1-2-4 k- and -1-2-4 k- respectively isA 1-2 B 1C 2 D 4

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Standard XII

Mathematics

Co-Linearity

Area of a rec...

Question

Area of a rectangle having vertices A, B, C, and D with position vectors and respectively is

(A) (B) 1

(C) 2 (D)

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Solution

The position vectors of vertices A, B, C, and D of rectangle ABCD are given as:

The adjacent sides and of the given rectangle are given as:

Now, it is known that the area of a parallelogram whose adjacent sides are is.

Hence, the area of the given rectangle is

The correct answer is C.

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Similar questions

Q. Area of a rectangle having vertices

A, B, C

and

D

with position vectors

-^i + \frac{1}{2}^j + 4^k

^i + \frac{1}{2}^j + 4^k

^i - \frac{1}{2}^j + 4^k

and

-^i - \frac{1}{2}^j + 4^k

Area of a rectangle having vertices $A (-^i + \frac{1}{2}^j + 4^k), B (^i + \frac{1}{2}^j + 4^k), C (^i - \frac{1}{2}^j + 4^k)$ and $D (-^i - \frac{1}{2}^j + 4^k)$ is

a) $\frac{1}{2}$
b) 1
c) 2
d) 4

Q. Let

\to a =^i + 2^j + 4^k, \to b =^i + λ^j + 4^k

and

\to c = 2^i + 4^j + (λ^{2} - 1)^k

be coplanar vectors. Then the non-zero vector

\to a \times \to c

is :

Q. At what value of the parameter n the vectors

\to a =^i + 2^j + 4^k

and

\to a =^i + 2^j + 2 n^k

are equal

Q. The unit vector which is perpendicular to the vectors

\to A =^i + 2^j -^k

and

\to B = 3^i - 2^j +^k

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Area of a rectangle having vertices A, B, C, and D with position vectors and respectively is (A) (B) 1 (C) 2 (D)

The position vectors of vertices A, B, C, and D of rectangle ABCD are given as: The adjacent sides and of the given rectangle are given as: Now, it is known that the area of a parallelogram whose adjacent sides are is. Hence, the area of the given rectangle is The correct answer is C.

Area of a rectangle having vertices A, B, C, and D with position vectors and respectively is

(A) (B) 1

(C) 2 (D)

The position vectors of vertices A, B, C, and D of rectangle ABCD are given as:

The adjacent sides and of the given rectangle are given as:

Now, it is known that the area of a parallelogram whose adjacent sides are is.

Hence, the area of the given rectangle is

The correct answer is C.