Recent questions in Vector Algebra

Using vector method, prove that if the diagonals of a parallelogram are equal in length, then it is a rectangle.

asked Feb 5, 2013 by meena.p

1 answer

Prove that the perpendicular bisectors of a triangle are concurrent.

asked Feb 5, 2013 by meena.p

1 answer

Prove that the altitudes of a triangle are concurrent.

asked Feb 5, 2013 by meena.p

1 answer

Using vector method, find the angle between two diagonals of a cube?

asked Feb 5, 2013 by meena.p

1 answer

Using vector method prove that : $a)\;\sin (A+B)=\sin A\cos B+\cos A\sin B$

asked Feb 5, 2013 by meena.p

1 answer

In a triangle ABC, prove that $\Large\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

asked Feb 5, 2013 by meena.p

1 answer

If $\Large\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are the $\large p^{th},q^{th}and\;r^{th}\;$ terms of an AP and $\bar{u}=(q-r)\bar{i}+(r-p)\bar{j}+(p-q)\bar{k}\;and\;\bar{v}=\large\frac{1}{a}\bar{i}+\frac{1}{b}\bar{j}+\frac{1}{c}\bar{k}$ then prove that $\bar{u}\; and\;\bar{v}$ are orthogonal vectors.

asked Feb 4, 2013 by meena.p

1 answer

Prove that the area of a paralellogram with diagonals $\bar{a}\;and\;\bar{b}\;is\;\frac{1}{2}|\bar{a} \times \bar{b}|$

asked Feb 4, 2013 by meena.p

1 answer

Let $\bar{a},\bar{b},\;and\;\bar{c}$ be three vectors such that $|\bar{a}|=3,|\bar{b}|=4,|\bar{c}|=5$ and each one of them being perpendicular to sum of the other two, find $|\bar{a}+\bar{b}+\bar{c}|$

asked Feb 4, 2013 by meena.p

1 answer

L and M are the mid-points of sides BC & DC of a paralellogram ABCD. Prove that $\overline{AL}+\overline{AM}=\frac{3}{2}\overline{AC}$

asked Feb 4, 2013 by meena.p

1 answer

Vectors $2\bar{i}-\bar{j}+2\bar{k}\;and\;\bar{i}+\bar{j}-3\bar{k}$ act along two adjacent sides of a parallelogram. Find the angle between the diagonals of the parallelogram.

asked Feb 4, 2013 by meena.p

1 answer

What is the area of the parallelogram having diagonals $3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$ ?

asked Feb 4, 2013 by meena.p

1 answer

Show that in a triangle ABC the perpendicular of the point $C$ from the line joining $the\:points\:A\:and\:B\:is\;\Large\frac{|\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}|}{|\bar{b}-\bar{a}|}$ (Hint : use area of triangle = $\frac{1}{2}$ bh)

asked Feb 4, 2013 by meena.p

0 answers

If $\hat{a}\;and\;\hat{b}$ are unit vectors inclined at an angle $\theta$ ,then prove that $(a)\;\cos \frac{\theta}{2}=\frac{1}{2}|\hat{a}+\hat{b}|\qquad(b)\;\tan \frac{\theta}{2}=\frac {|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}$

asked Feb 4, 2013 by meena.p

1 answer

Prove that angle in a semi-circle is a right angle.

asked Feb 4, 2013 by meena.p

1 answer

If $\bar{a}\;and\;\bar{b}$ are vectors,prove that $|\bar{a} \times \bar{b}|^2+(\bar{a}.\bar{b})^2=|\bar{a}|^2.|\bar{b}|^2$

asked Feb 4, 2013 by meena.p

1 answer

Prove Cauchy - Schawarz inequality : $(\bar{a}.\bar{b})^2\leq|\bar{a}|^2.|\bar{b}|^2$

asked Feb 4, 2013 by meena.p

0 answers

Prove the triangle inequality $\bigg|\overrightarrow{a}+\overrightarrow{b}\bigg|\leq\bigg|\overrightarrow{a}\bigg|+\bigg|\overrightarrow{b}\bigg|$

asked Feb 4, 2013 by meena.p

1 answer

If $\overrightarrow {a}+ \overrightarrow {b}+ \overrightarrow {c}=\overrightarrow 0$ show that $\overrightarrow {a} \times \overrightarrow {b}=\overrightarrow {b} \times \overrightarrow {c}=\overrightarrow {c} \times \overrightarrow {a}$

asked Feb 4, 2013 by meena.p

1 answer

If $\bar{\alpha}=3\bar{i}-\bar{j}\;and\;\bar{\beta}=2\bar{i}+\bar{j}-\bar{k}.$ Express $\bar{\beta}$ as a sum of two vectors $\bar{\beta_1}\;and\;\bar{\beta_2},\;where \; \bar{\beta_1}$ is parallel to $\bar{\alpha}\;and\; \bar{\beta_2}$ is prependicular to $\bar{\alpha}$

asked Feb 4, 2013 by meena.p

1 answer