Recent questions tagged p88

Verify $(\overrightarrow{a}\times\overrightarrow{b}) \times (\overrightarrow{c}\times\overrightarrow{d})=[\overrightarrow{a} \overrightarrow{b} \overrightarrow{d} ] \overrightarrow{c} - [\overrightarrow{a} \overrightarrow{b} \overrightarrow{c} ] \overrightarrow{d}$, For $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},\overrightarrow{ b}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{c}=\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}, \overrightarrow{d}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{2k}.$

asked Apr 6, 2013 by poojasapani_1

1 answer

Find$ (\overrightarrow{a}\times\overrightarrow{b}) . (\overrightarrow{c}\times\overrightarrow{d}) $if $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}, \overrightarrow{b}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{c}=\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}, \overrightarrow{d}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{2k}$

asked Apr 6, 2013 by poojasapani_1

1 answer

Prove that $(\overrightarrow{a}\times\overrightarrow{b}) . (\overrightarrow{c}\times\overrightarrow{d}) + (\overrightarrow{b}\times\overrightarrow{c}) . (\overrightarrow{a}\times\overrightarrow{d}) + (\overrightarrow{c}\times\overrightarrow{a}) . (\overrightarrow{b}\times\overrightarrow{d})=0$

asked Apr 6, 2013 by poojasapani_1

1 answer

For any vector $\overrightarrow{a}$ Prove that $\overrightarrow{i} \times (\overrightarrow{a}\times\overrightarrow{i})+ \overrightarrow{j} \times (\overrightarrow{a}\times\overrightarrow{j})+ \overrightarrow{k } \times(\overrightarrow{a}\times\overrightarrow{k})=\overrightarrow{2a}$

asked Apr 6, 2013 by poojasapani_1

1 answer

Prove that $( \overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c}= \overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})$ if $ \overrightarrow{a}$ and $ \overrightarrow{c}$ are collinear. (Where vector triple product is non-zero).

asked Apr 5, 2013 by poojasapani_1

1 answer

If $ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{5k}, \overrightarrow{b}= -\overrightarrow{1}+ \overrightarrow{j}+ \overrightarrow{2k}$ and $ \overrightarrow{c}= \overrightarrow{4i}- \overrightarrow{2j}+ \overrightarrow{3k}, $ Show that $( \overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c} \neq \overrightarrow{a} \times( \overrightarrow{b}\times \overrightarrow{c})$

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove thet $ \overrightarrow{a}\times( \overrightarrow{b}\times \overrightarrow{c})+ \overrightarrow{b}\times( \overrightarrow{c}\times{a})+ \overrightarrow{c}\times( \overrightarrow{a}\times \overrightarrow{b})=0$

asked Apr 5, 2013 by poojasapani_1

1 answer

if $\ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{k} , \overrightarrow{b}= -\overrightarrow{2i}+ \overrightarrow{5k}, \overrightarrow{c}= \overrightarrow{j}- \overrightarrow{3k}. $ Verify that $ \overrightarrow{a}\times ( \overrightarrow{b}\times \overrightarrow{c})= (\overrightarrow{a}. \overrightarrow{c}) \overrightarrow{b}- (\overrightarrow{a}. \overrightarrow{b})c$

asked Apr 5, 2013 by poojasapani_1

1 answer

Show that the points$(1 ,3 ,1), (1, 1, -1),(-1,1, 1),(2 ,2,- 1) $ are lying on the same plane.(Hint : It is enough to prove any three vectors formed by these four points are coplanar).

asked Apr 5, 2013 by poojasapani_1

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (ii) } A = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \text{ , } B = \begin{bmatrix} 1 & 5 & 7 \end{bmatrix} $$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix}$, then verify that $ (ii) ( A - B )' = A' - B' $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} $then verify that $ (ii) (A-B)' = A' - B'$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

(iii) Find the transpose of the matrix \begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix}

asked Mar 1, 2013 by sharmaaparna1

1 answer

Find the transpose of the following matrices: $ \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$

asked Mar 1, 2013 by balaji.thirumalai

1 answer

Find the transpose of each of the following matrices :$ (i) \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix}$

asked Mar 1, 2013 by balaji.thirumalai

1 answer

Find the transpose of each of the following matrices : $$ \text{ (i) } \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix} \qquad \qquad (ii) \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} \qquad \qquad (iii)\begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix} $$

asked Nov 25, 2012 by pady_1

1 answer

if $ A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} \text{, then verify that } $ $$ \text{ (i) } (A+B)' = A' + B' $$

asked Nov 25, 2012 by pady_1

1 answer

If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix} \text{ , then verify that } $$ \text{ (i) } (A + B )' = A' + B' \qquad \qquad $

asked Nov 25, 2012 by pady_1

1 answer

If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix}$, then find $(A + 2B)'$

asked Nov 25, 2012 by pady_1

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$

asked Nov 25, 2012 by pady_1

1 answer

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