Question

Find the area of parallelogram formed by vector If a vector is equals to 3 ICAP + 2 J cap and b vector is equals to minus 3 ICAP + 7 j
cap

Answer 1

Answer:

Area of the parallelogram is $7\sqrt{13}$.

Explanation:

In the question,

We have two vectors given to us,

$a=3i+2j\\and,\\b=-3i+7j$

So,

We also know that,

Area of parallelogram, A is given by,

$A=|a||b|sin\theta =|a\times b|$

So,

$Area, A=|a||b|sin\theta \\So,\\|a|=\sqrt{(3)^{2}+(2)^{2}} =\sqrt{13} \\Also,\\|b|=\sqrt{(-3)^{2}+(7)^{2}} =\sqrt{58} \\\\Now,\\\\tan\theta=\frac{7}{-3}\\So,\\ sin\theta=\frac{7}{\sqrt{58} }$

Now,

Area will be,

$A=\sqrt{13}\sqrt{58}\times\frac{7}{\sqrt{58} }\\A=7\sqrt{13}$

Therefore, the area of the parallelogram is $7\sqrt{13}$.

Answer 2

Explanation:

Here is your answer

area of parallelogram = 27 sq. units