Two adjacent sides of a parallelogram are $2\hat{\mathrm{i}}-4\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ and $\hat{\mathrm{i}}-2\hat{\mathrm{j}}-3\widehat{\mathrm{k}.}$ What is the magnitude of dot product of vectors which represent its diagonals?

$1.$ $\left(a+b\right)·\left(a-b\right)={\left|a\right|}^2-{\left|b\right|}^2$

$2.$ $\left(\left|a+b\right|\right)\left(\left|a-b\right|\right)={\left|a\right|}^2-{\left|b\right|}^2$

$3.$ $\left|a·b\right|+\left|a\times b\right|={\left|a\right|}^2{\left|b\right|}^2$

Which of the above statements are correct?

$1.$ The magnitude of $a\times b$ is same as the area of a triangle with sides $a$ and $b$.

$2.$ If $a\times b=0,$ where $a\ne 0, b\ne 0,$ then $a=\lambda b.$

Which of the above statements is/are correct?