Question

The area of a parallelogram whose diagonals are P= 2î +3j and 0 = i +4j is

Answer 1

Answer:

$Area=+\frac{5}{2}\hat k~~m^2=2.5~m^2$

Explanation:

Area of a parallelogram with it's diagonals given is

$Area=\frac{1}{2}({d_1} \times d_2)$

Here, d₁ = 2i + 3j

And, d₂ = 1i + 4j

Hence, (d₁ × d₂)

$\left[\begin{array}{ccc}i&j&k\\2&3&0\\1&4&0\end{array}\right] \\\\\\=(0-0)\hat i\,-(0-0)\hat j\,+(8-3 )\hat k\\\\=+5\hat k\,\,\,\,m^2$

Hence, area of parallelogram,

$Area=\frac{1}{2}\times (+5\hat k)=+\frac{5}{2}\hat k~~m^2$