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Recent questions tagged sec-1

Derive the equation of the plane in the intercept form.

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector cartesian equation of the plane passing through the points with position vectors $\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{2k}, \overrightarrow{2i}-\overrightarrow{2j}-\overrightarrow{2k},$ and $\overrightarrow{7i}+\overrightarrow{k}.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector cartesian equation of the plane containing the line $\large\frac{x-2}{2}=\frac{y-2}{3}=\frac{z-1}{-2}$ and passing through the point $(-1 , 1 , -1 )$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane through the points $(1 , 2 , 3 )$and $(2 , 3 , 1 )$ perpendicular to the plane $ 3x-2y+4z-5=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane passing through the points $ A(1 , -2 , 3 )$ and $B(-1 , 2 , -1 )$ and is parallel to the line $ \large\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-1}{4}.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation to the plane through the point $(-1 , 3 , 2 ) $ and perpendicular to the planes $x+2y+2z=5$ and $3x+y+2z=8.$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane through the point $(1 , 3 , 2 ) $ and parallel to the lines $\large\frac{x+1}{2}=\frac{y+2}{-1}=\frac{z+3}{3}$ and parallel to the line $\large\frac{x-2}{1}=\frac{y+1}{2}=\frac{z+2}{2}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane containing the line $\Large\frac{x-2}{2}=\frac{y-2}{3}=\frac{z-1}{3}$ and parallel to the line $\Large\frac{x+1}{3}=\frac{y-1}{2}=\frac{z+1}{1}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane through the point $(2 , -1 , 4 )$ and parallel to the plane $\overrightarrow{r} . (\overrightarrow{4i}-\overrightarrow{12j}-\overrightarrow{3k})=7.$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the equation of the plane through the point whose $p.v. $ is $\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{k}$ and perpendicular to the vector $\overrightarrow{4i}+\overrightarrow{2j}-\overrightarrow{3k}$

asked Apr 7, 2013 by poojasapani_1

1 answer

The foot of the perpendicular drawn from the origin to the plane is $(8 , -4 , 3 )$ find the equation of the plane.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the length of the perpendicular frome the origin to the plane$\overrightarrow{r} . (\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{12k})=26$.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the unit normal vectors to the plane $2x-y+2z=5$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of a plane which is at a distance of $18$ units from the origin and which is normal to the vector $\overrightarrow{2i}+\overrightarrow{7j}+\overrightarrow{8k}$

asked Apr 7, 2013 by poojasapani_1

1 answer

If the point $(\lambda , 0 , 3 ), (1 , 3 , -1 )$ and $(-5 , -3 , 7 )$ are collinear than find $\lambda$.

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that $(2 , -1 ,3 ),(1 ,-1, 0 )$ and $(3, -1, 6 )$ are collinear.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the shortest distance between the skew lines $\large\frac{x-6}{3}=\frac{y-7}{-1}=\frac{z-4}{1}$ and $\large\frac{x}{-3}=\frac{y+9}{2}=\frac{z-2}{4}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that the lines $\large \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{3}$ and $\large\frac{x-2}{1}=\frac{y-1}{2}=\frac{-z-1}{1}$ intersect and find their point of intersection.

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that the following two lines are skew lines: $\overrightarrow{r}=(\overrightarrow{3i}+\overrightarrow{5j}+\overrightarrow{7k})+ t (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{k})$ and $\overrightarrow{r}=(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}) + s (\overrightarrow{7i}-\overrightarrow{6j}+\overrightarrow{7k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the shortest distance between the parallel lines $\large\frac{x-1}{-1}=\frac{y}{3}=\frac{z+3}{2} $ and $\large\frac{x-3}{-1}=\frac{y+1}{3}=\frac{z-1}{2} $

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the shortest distance between the parallel lines $\overrightarrow{r}=(\overrightarrow{2i}-\overrightarrow{j}-\overrightarrow{k}) + t (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$ and $\overrightarrow{r}=(\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{k}) + s (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the angle between the lines $\overrightarrow{r}=\overrightarrow{5i}-\overrightarrow{7j}+\mu (-\overrightarrow{i}+\overrightarrow{4j}+\overrightarrow{2k}) \overrightarrow{r}=-\overrightarrow{2i}+\overrightarrow{k}+\lambda (\overrightarrow{3i}+\overrightarrow{4k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the angle between the following lines. $\large\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-4}{6}$ and $ x+1=\large\frac{y+2}{2}=\frac{z-4}{2}$

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line joining the points $(1 , -2 , 1 )$ and $(0 , -2 , 3 ).$

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line through the point $(3 , -4 , -2 )$ and parallel to vector $\overrightarrow{9i} +\overrightarrow{6j} +\overrightarrow{2k}$.

asked Apr 6, 2013 by poojasapani_1

1 answer

Find direction consines of the line joinong $(2 , -3 , 1 )$and $(3 , 1 , -2 ).$

asked Apr 6, 2013 by poojasapani_1

1 answer

A vector $\overrightarrow{r}$ has length $35\sqrt{2}$ and direction ratios $(3 , 4 , 5 ),$ Find the direction consines and components of $\overrightarrow{r}$.

asked Apr 6, 2013 by poojasapani_1

1 answer

What are the d . c . s of the vector equally inclined to the axes?

asked Apr 6, 2013 by poojasapani_1

1 answer

Can a vector have direction angles $45^{\circ}, 60^{\circ}, 120^{\circ}$?

asked Apr 6, 2013 by poojasapani_1

1 answer

Can a vector have direction angles $30^{\circ},45^{\circ},60^{\circ}$?

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the d . c. s of a vector whose direction ratios are $2 , 3 , -6.$

asked Apr 6, 2013 by poojasapani_1

1 answer

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

Prove that $\mid[\overrightarrow{a} \overrightarrow{b} \overrightarrow{c}]\mid=a b c $ if and only if $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are mutually perpendicular.

asked Apr 5, 2013 by poojasapani_1

1 answer

The volume of a parallelopiped whose edges are represented by $-\overrightarrow{12i}+\lambda\overrightarrow{k}, \overrightarrow{3j}-\overrightarrow{k}, \overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{15k} $ is $546;\quad$ find the value of $\lambda$.

asked Apr 5, 2013 by poojasapani_1

1 answer

Show that the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are coplanar if and only if $\overrightarrow{a}+\overrightarrow{b},\overrightarrow{b}+\overrightarrow{c},\overrightarrow{c}+\overrightarrow{a}$ are coplanar.

asked Apr 5, 2013 by poojasapani_1

1 answer

Find the magnitude and direction cosines of the moment about the point $(1, -2 ,3)$ of a force $\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{6k}$ Whose line of action passes through the origin.

asked Apr 5, 2013 by poojasapani_1

1 answer

Show that the torque about the point $ A(3, -1, 3 )$ of a force $\overrightarrow{4i}+\overrightarrow{2j}\overrightarrow{k}$ throught the point $\overrightarrow\;B(5, 2, 4)$ is $\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{8k}$.

asked Apr 5, 2013 by poojasapani_1

1 answer

Forces $\overrightarrow{2i}+\overrightarrow{7j}, \overrightarrow{2i}-\overrightarrow{5j}+\overrightarrow{6k}, \overrightarrow{-i}+\overrightarrow{2j}-\overrightarrow{k}$ act at a point $P$ Whose position vector is $\overrightarrow{4i}-\overrightarrow{3j}-\overrightarrow{2k}.$ Find the moment of the resultant of three forces acting at $P$ about the point $Q$ whose position vector is $\overrightarrow{6i}+\overrightarrow{j}-\overrightarrow{3k}.$

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove that sin $(A - B)$= sin $ A$ cos $B$ - cos $A$ sin $B$.

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove that twice the area of parallelogram is equal to the area of another parallelogram formed by taking as its adjacent sides the diagonals of the former parallelogram.

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove by the vector method, thet the parallelogram on the same base and between the same parallels are equal in area.

asked Apr 5, 2013 by poojasapani_1

1 answer

Find the area of the triangle whose vertices are $(3, -1, 2), (1 ,-1, -3 ), $and $(4, -3, 1) $

asked Apr 5, 2013 by poojasapani_1

1 answer

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