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Questions >> TN XII Math >> Vector Algebra

Let $\overrightarrow{u},\overrightarrow{v}$ and $\overrightarrow{w}$ be vector such that $\overrightarrow{u}+\overrightarrow{v}+\overrightarrow{w}=\overrightarrow{0}.$ If $|\overrightarrow{u}|=3, |\overrightarrow{v}|=4$ and $|\overrightarrow{w}|=5$ than find $\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}+\overrightarrow{w}.\overrightarrow{u}$

asked Apr 3, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a}+\overrightarrow{b}|=60, |\overrightarrow{a}-\overrightarrow{b}|=40$ and $|\overrightarrow{b}|=46$ find $|\overrightarrow{a}|.$

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}\;,\overrightarrow{b}\;,\overrightarrow{c}$ are three mutually perpendicular unit vectors,than prove that $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{3}$

asked Apr 3, 2013 by poojasapani_1

1 answer

If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is $\sqrt{3}$ .

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the value of $m$ for which the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{9k}$ and $\overrightarrow{b}=\overrightarrow{i}+\overrightarrow{mj}+\overrightarrow{3k}$ are perpendicular

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\hat{a}$ and $\hat{b}$ are unit vectors inclined at an angle $\theta$ ,than prove that cos $\Large\frac{\theta}{2}$ = $\Large\frac{1}{2}$ $|\hat{a}$ + $\hat{b}|$

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\hat{a}$ and $\hat{b}$ are unit vectors inclined at an angle $\theta$ ,than prove that tan $\large\frac{\theta}{2}$ = $\large\frac{|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}$

asked Apr 2, 2013 by poojasapani_1

1 answer

Show that the vector $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is equally inclined with the coordinate axes.

asked Apr 2, 2013 by poojasapani_1

1 answer

Find the angles which the vector $\overrightarrow{i}-\overrightarrow{j}+\sqrt{2}\overrightarrow{k}$ makes with the coordinate axes.

asked Apr 2, 2013 by poojasapani_1

1 answer

Find the value of $m$ for which the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{9k}$ and $\overrightarrow{b}=\overrightarrow{i}+\overrightarrow{mj}+\overrightarrow{3k}$ are parallel

asked Apr 2, 2013 by poojasapani_1

1 answer

Find $\lambda$ so that the vectors $\overrightarrow{2i}+\overrightarrow{\lambda\;j}+\overrightarrow{k}$ and $\overrightarrow{i}- \overrightarrow{2j} +\overrightarrow{k}$ are perpendicular to each other.

asked Apr 2, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a} =\overrightarrow{i} + \overrightarrow{j}+\overrightarrow{2k}\; and\; \overrightarrow{b}=\overrightarrow{3i} +\overrightarrow{2j}-\overrightarrow{k}$ find $(\overrightarrow{a}+\overrightarrow{3b}) . (\overrightarrow{2a}-\overrightarrow{b})$

asked Apr 2, 2013 by poojasapani_1

1 answer

Find $\overrightarrow{a} .\overrightarrow{b}$ when $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{2j}-\overrightarrow{k}$ and $\overrightarrow{b} =\overrightarrow{6i}-\overrightarrow{3j}+\overrightarrow{2k}$

asked Apr 2, 2013 by poojasapani_1

1 answer

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