Question

The area of parallelogram represented by the vectors $A=2\hat{i}+3\hat{j}andB=\hat{i}+4\hat{j}$ is

• A. $14$ unit
• B. $7.5$ unit
• C. $10$ unit
• D. $5$ unit.

Answer 1

The correct option is D $5$ unit.

Given$A=2i+3jandB=i+4j$ .

Area of paralleogram $AxB=(2i+3j+0k)\times (i+4j+0k)$

For i component we have,

$(3\times 0)-(4\times 0)=0$

For j component we have,

$(0\times 2)-(1\times 0)=0$

For k component we have,

$(2\times 4)-(1\times 3)=5$.

Now take the magnitude of this vector to find the area of the parallelogram:

$A\times B$ = Whole root of $0^2+0^2+5^2$

= $0+0+5=5units$