Recent questions in Vector Algebra

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ represent the vertices of a triangle,then show that $\frac{1}{2}\mid\overrightarrow{b}\times\overrightarrow{c}+\overrightarrow{c}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}\mid$ gives the vector area of the triangle .Hence deduce the condition that the three points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are collinear.Also find the unit vector normal to the plane of the triangle.

asked Jan 17, 2013 by sreemathi.v

1 answer

Prove that in any triangle ABC, $cos A=\large \frac{b^2+c^2-a^2}{2bc}$ , $where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,find the area of the triangle ABC with vertices $A(1,2,3),B(2,-1,4)$ and $C(4,5,-1).$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the sine of the angle between the vectors $\overrightarrow{a}=3\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=-2\hat i+2\hat j+4\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,$ show that $\overrightarrow{a} \times \overrightarrow{b}=\overrightarrow{b} \times \overrightarrow{c} =\overrightarrow{c} \times \overrightarrow{a}$ .Interpret the result geometrically?

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the angle between the vectors $2\hat i\;-\hat j\;-\hat k$ and $3\hat i\;+4\hat j\;+\hat k$ .

asked Jan 17, 2013 by sreemathi.v

1 answer

FInd a vector of magnitude 6 ,which is perpendicular to both the vectors $2\hat i-\hat j+2\hat k$ and $4\hat i-\hat j+3\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

A vector $\overrightarrow{r}$ has magnitude 14 and direction ratios 2,3,-6.Find the direction cosines and components of $\overrightarrow{r}$ ,given that $\overrightarrow{r}$ makes an acute angle with x-axis.

asked Jan 17, 2013 by sreemathi.v

1 answer

A vector $\overrightarrow{r}$ is inclined at equal angles to the three axes.If the magnitude of $\overrightarrow{r}$ is $2\sqrt 3$ units,find $\overrightarrow{r}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,find the value of k such that the points $(k,-10,3),(1,-1,3)$ and $(3,5.3)$ are collinear.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are the position vectors of $A$ and $B$ ,respectively,find the position vector of a point $C$ in $BA$ produced such that $BC=1.5BA$ .

asked Jan 17, 2013 by sreemathi.v

1 answer

Find a unit vector in the direction of $\overrightarrow{PQ},$ where $P$ and $Q$ have co-ordinates $(5,0,8)$ and $(3,3,2)$ ,respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}=\hat i-\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i-\hat j-2\hat k,$ then find the unit vector in the direction of $6 \overrightarrow{b}$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the unit vector in the direction of sum of vectors $\overrightarrow{a}=2\hat i+\hat j+\hat k\;and\;\overrightarrow{b}=2\hat j-\hat k$

asked Jan 16, 2013 by sreemathi.v

1 answer

Represent graphically a displacement of 40 km, 30° east of north.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Classify the following measures as scalars and vectors. $(i)\;10\: kg$

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Classify the following as scalar and vector quantities. $(i)\;$ time period.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

In Fig 10.6 (a square), identify the following vectors. $(i)\; Coinitial\qquad (ii)\; Equal\qquad (iii)\; Collinear\; but\; not\; equal$

asked Dec 7, 2012 by thanvigandhi_1

1 answer