Let A1 - 3- A2 - 5- and A1 - A2 - 5- A1 is same as A1 and A2 is same as A2- The value of 2A1 - 3A2-3A1 - 2A2 is- report the magnitude-

For vector A_1 + A_2, we have A_1 + A_2 ^2 = (A_1 + A_2).(A_1 + A_2) [∵ x . x = x ^2] ⇒ A_1 + A_2 ^2 = A_1 ^2 + A_2 ^2 nbsp;+ 2A_1.A_2 Given, A_1 = 3, A ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Adjoint of a Matrix

Let A1 = 3, A...

Question

Let $| \begin{matrix} A_{1} \end{matrix} | = 3, | \begin{matrix} A_{2} \end{matrix} | = 5,$ and $| \begin{matrix} A_{1} + A_{2} \end{matrix} | = 5$ . $A_{1}$ is same as $_{1}$ and $A_{2}$ is same as $_{2}$ . The value of $(2 A_{1} + 3 A_{2}) . (3 A_{1} - 2 A_{2})$ is: (report the magnitude).

Open in App

Solution

For vector $A_{1} + A_{2},$ we have
${| \begin{matrix} A_{1} + A_{2} \end{matrix} |}^{2} = (A_{1} + A_{2}) . (A_{1} + A_{2}) [∵ x . x = {| \begin{matrix} x \end{matrix} |}^{2}]$
$\Rightarrow {| \begin{matrix} A_{1} + A_{2} \end{matrix} |}^{2} = {| \begin{matrix} A_{1} \end{matrix} |}^{2} + {| \begin{matrix} A_{2} \end{matrix} |}^{2} + 2 A_{1} . A_{2}$
Given, $| \begin{matrix} A_{1} \end{matrix} | = 3, | \begin{matrix} A_{2} \end{matrix} | = 5$ and $| \begin{matrix} A + A_{2} \end{matrix} | = 5$
So, we have
$(5)^{2} = 9 + 25 + 2 A_{1} . A_{2}$
$\Rightarrow A_{1} . A_{2} = - \frac{9}{2}$
Now, $(2 A_{1} + 3 A_{2}) . (3 A_{1} - 2 A_{2})$
$= 6 {| \begin{matrix} A_{1} \end{matrix} |}^{2} - 4 A_{1} . A_{2} + 9 A_{1} . A_{2} - 6 {| \begin{matrix} A_{2} \end{matrix} |}^{2}$
$= 6 {| \begin{matrix} A_{1} \end{matrix} |}^{2} - 6 {| \begin{matrix} A_{2} \end{matrix} |}^{2} + 5 A_{1} . A_{2}$
Substituting values, we have
$(2 A_{1} + 3 A_{2}) . (3 A_{1} - 2 A_{2})$
$= 6 (9) - 6 (25) + 5 (- \frac{9}{2}) = - 118.5$

Suggest Corrections

Similar questions

Q. Let

|_{1} | = 3, |_{2} | = 5

and

|_{1} +_{2} | = 5

. The value of

(2_{1} + 3_{2}) . (3_{1} - 2_{2})

is,

Q. If

_{1}

and

_{2}

are two two non-collinear unit vectors , then the value of

(_{1} -_{2}) . (\to 2 a_{1} +_{2})

which is not possible is

If $a_{1}, a_{2}, a_{3}, a_{4}$ are the coefficients of any four

consecutive terms in the expansion of ( $1 + x)^{n}$ , then

$\frac{a_{1}}{a_{1} + a_{2}}$ + $\frac{a_{3}}{a_{3} + a_{4}}$ =

If $a_{1}, a_{2}, a_{3}, a_{4}$ are the magnitude of the coordinates at which the circle cuts the axes as shown in the figure. Then what the sum of x and y intercepts.

Q. If

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

then

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

Join BYJU'S Learning Program

Let |A1|=3,|A2|=5, and |A1+A2|=5. A1 is same as −→A1 and A2 is same as −→A2. The value of (2A1+3A2).(3A1−2A2) is: (report the magnitude).

Let $| \begin{matrix} A_{1} \end{matrix} | = 3, | \begin{matrix} A_{2} \end{matrix} | = 5,$ and $| \begin{matrix} A_{1} + A_{2} \end{matrix} | = 5$ . $A_{1}$ is same as $_{1}$ and $A_{2}$ is same as $_{2}$ . The value of $(2 A_{1} + 3 A_{2}) . (3 A_{1} - 2 A_{2})$ is: (report the magnitude).