Question 78: Motion in 2D & Vectors

Question

Let $$\left| {\mathop {{A_1}}\limits^ 	o  } ight| = 3$$,  $$\left| {\mathop {{A_2}}\limits^ 	o  } ight| = 5$$ and $$\left| {\mathop {{A_1}}\limits^ 	o   + \mathop {{A_2}}\limits^ 	o  } ight| = 5$$. The
value of $$\left( {2\mathop {{A_1}}\limits^ 	o   + 3\mathop {{A_2}}\limits^ 	o  } ight)\left( {3\mathop {{A_1}}\limits^ 	o   - \mathop {2{A_2}}\limits^ 	o  } ight)$$
is :-

Accepted Answer

$$\left| {\overrightarrow {{A_1}} } ight| = 3,\left| {\overrightarrow {{A_2}} } ight| = 5\,and\,\left| {\overrightarrow {{A_1}}  + \overrightarrow {{A_2}} } ight| = 5$$
$$\,\left| {\overrightarrow {{A_1}}  + \overrightarrow {{A_2}} } ight| = {\left| {\overrightarrow {{A_1}} } ight|^2} + {\left| {\overrightarrow {{A_2}} } ight|^2} + 2\left| {\overrightarrow {{A_1}} } ight|\left| {\overrightarrow {{A_2}} } ight|\cos 	heta $$
$$\cos 	heta  =  - {3 \over {10}}$$
$$\left( {2\overrightarrow {{A_1}}  + 3\overrightarrow {{A_2}} } ight).\left( {3\overrightarrow {{A_1}}  - 2\overrightarrow {{A_2}} } ight)$$
= $$6{\left| {\overrightarrow {{A_1}} } ight|^2} + 9\overrightarrow {{A_1}} .\overrightarrow {{A_2}}  - 4\overrightarrow {{A_1}} .\overrightarrow {{A_2}}  - 6{\left| {\overrightarrow {{A_2}} } ight|^2}$$
= - 118.5

Answer

–118.5

Answer

–112.5

Answer

–99.5

Answer

–106.5

Motion in 2D & Vectors

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