Question

the area of the parallelogram whose sides are represented by vector i^+3k^ and i+2j-k^ is

Answer 1

Given :

• Sides of parallelogram -

1. i^ + 3k
2. i^ + 2j^ - k^

To find :

• Area of the parallelogram.

Solution :

• We are given vectors which represent two adjacent sides of a parallelogram.
• To find the area, we take the cross product of the given vectors.
• The magnitude of the cross product will give us the area of the parallelogram.
• Let C be a vector which is the cross product of the given two vectors.

• ∴ Vector C = (i^ + 3k^) x (i^ +2j^ - k^)

•  $Vector C = \left[\begin{array}{ccc}i^&j^&k^\\1&0&3\\1&2&-1\end{array}\right]$

                         = -6i^ +4j^ + 2k^

• Now, Area = Magnitude of vector C

                           = $\sqrt{36 + 16 + 4}$

                 $Area = \sqrt{56}$

Answer : The area of the parallelogram will be $\sqrt{56}$ sq. units

Answer 2

Answer:√56

Explanation:

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