Recent questions tagged p458

Write down a unit vector in XY plane, making an angle of 30 degress with the positive direction of $x$ axis.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the scalar components and magnitude of the vector joining the points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = \overrightarrow b + \overrightarrow c$, then is it true that $| \overrightarrow a | = | \overrightarrow b | + | \overrightarrow c |$? Justify your answer.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the value of $x$ for which $x(\hat i + \hat j +\hat k)$ is a unit vector.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find a vector of magnitude $5$ units, and parallel to the resultant of the vectors $\overrightarrow a = 2\hat i + 3 \hat j - \hat k$ and $\overrightarrow b = \hat i - 2\hat j + \hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are $(2\overrightarrow a + \overrightarrow b)$ and $(\overrightarrow a - 3\overrightarrow b)$ externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

asked Dec 5, 2012 by thanvigandhi_1

1 answer

The two adjacent sides of a parallelogram are $2\hat i - 4\hat j + 5\hat k$ and $ \hat i - 2\hat j - 3\hat k$ . Find the unit vector parallel to its diagonal. Also, find its area.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $ \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3} $

asked Dec 5, 2012 by thanvigandhi_1

1 answer

The scalar product of the vector $\hat i + \hat j + \hat k$ with a unit vector along the sum of vectors $2\hat i + 4 \hat j − 5\hat k$ and $λ\hat i + 2 \hat j + 3\hat k$ is equal to one. Find the value of $ λ.$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $ \overrightarrow a, \overrightarrow b, \overrightarrow c, $ are mutually perpendicular vectors of equal magnitudes, show that the vector $ \overrightarrow a + \overrightarrow b + \overrightarrow c$ is equally inclined to $ \overrightarrow a, \overrightarrow b and \overrightarrow c$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Ask Questions, Get Answers

Write down a unit vector in XY plane, making an angle of 30 degress with the positive direction of $x$ axis.

Find the scalar components and magnitude of the vector joining the points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

If $\overrightarrow a = \overrightarrow b + \overrightarrow c$, then is it true that $| \overrightarrow a | = | \overrightarrow b | + | \overrightarrow c |$? Justify your answer.

Find the value of $x$ for which $x(\hat i + \hat j +\hat k)$ is a unit vector.

Find a vector of magnitude $5$ units, and parallel to the resultant of the vectors $\overrightarrow a = 2\hat i + 3 \hat j - \hat k$ and $\overrightarrow b = \hat i - 2\hat j + \hat k$

If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \((2\overrightarrow a + \overrightarrow b)\) and \((\overrightarrow a - 3\overrightarrow b)\) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

The two adjacent sides of a parallelogram are \(2\hat i - 4\hat j + 5\hat k\) and \( \hat i - 2\hat j - 3\hat k\) . Find the unit vector parallel to its diagonal. Also, find its area.

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $ \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3} $

The scalar product of the vector \(\hat i + \hat j + \hat k\) with a unit vector along the sum of vectors \(2\hat i + 4 \hat j − 5\hat k\) and \(λ\hat i + 2 \hat j + 3\hat k\) is equal to one. Find the value of \( λ.\)

If \( \overrightarrow a, \overrightarrow b, \overrightarrow c, \) are mutually perpendicular vectors of equal magnitudes, show that the vector \( \overrightarrow a + \overrightarrow b + \overrightarrow c\) is equally inclined to \( \overrightarrow a, \overrightarrow b and \overrightarrow c\).