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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

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

-^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

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

\to c = 2^i + 4^j + (λ^{2} - 1)^k

be coplanar vectors. Then the non-zero vector

\to a \times \to c

Q. At what value of the parameter n the vectors

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

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

Q. The unit vector which is perpendicular to the vectors

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

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

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