Question

verify that | a × b | = | a | × | b | if a= 2/-5 , b = 3/4​

Answer 1

Given:

$a = \frac{2}{ - 5}$

$b = \frac{3}{4}$

To verify:

$|a \times b| = |a| \times |b|$

Solution:

Let us first solve for L. H. S.

$\longrightarrow{\green{}}$ $|a \times b|$

$\longrightarrow{\green{}}$ $| \frac{2}{ - 5} \times \frac{3}{4} |$

$\longrightarrow{\green{}}$ $| \frac{6}{ - 20} |$

$\longrightarrow{\green{}}$ $| \frac{3}{ - 10} |$

$\longrightarrow{\green{}}$ $\frac{3}{10}$

Now, let us solve for R. H. S.

$\longrightarrow{\green{}}$ $|a| \times |b|$

$\longrightarrow{\green{}}$ $| \frac{2}{ - 5} | \times | \frac{3}{4} |$

$\longrightarrow{\green{}}$ $\frac{2}{5} \times \frac{3}{4}$

$\longrightarrow{\green{}}$ $\frac{6}{20}$

$\longrightarrow{\green{}}$ $\frac{3}{10}$

$\longrightarrow{\green{}}$ L. H. S.

Since L. H.S. = R. H. S.

$\boxed{ Hence \:verified. }$

$\sf\purple{Note:}$ The absolute value of a number is never negative.

Answer 2

Answer:

Given:

a = \frac{2}{ - 5}a=

−5

2

b = \frac{3}{4}b=

4

3

To verify:

|a \times b| = |a| \times |b|∣a×b∣=∣a∣×∣b∣

Solution:

Let us first solve for L. H. S.

\longrightarrow{\green{}}⟶ |a \times b|∣a×b∣

\longrightarrow{\green{}}⟶ | \frac{2}{ - 5} \times \frac{3}{4} |∣

−5

2

×

4

3

∣

\longrightarrow{\green{}}⟶ | \frac{6}{ - 20} |∣

−20

6

∣

\longrightarrow{\green{}}⟶ | \frac{3}{ - 10} |∣

−10

3

∣

\longrightarrow{\green{}}⟶ \frac{3}{10}

10

3

Now, let us solve for R. H. S.

\longrightarrow{\green{}}⟶ |a| \times |b|∣a∣×∣b∣

\longrightarrow{\green{}}⟶ | \frac{2}{ - 5} | \times | \frac{3}{4} |∣

−5

2

∣×∣

4

3

∣

\longrightarrow{\green{}}⟶ \frac{2}{5} \times \frac{3}{4}

5

2

×

4

3

\longrightarrow{\green{}}⟶ \frac{6}{20}

20

6

\longrightarrow{\green{}}⟶ \frac{3}{10}

10

3

\longrightarrow{\green{}}⟶ L. H. S.

Since L. H.S. = R. H. S.

\boxed{ Hence \:verified. }

Henceverified.

\sf\purple{Note:}Note: The absolute value of a number is never negative.