Recent questions tagged ch10

Show that the vector $ \hat i + \hat j + \hat k$ is equally inclined to the axes OX, OY and OZ.

asked Dec 6, 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 $ \hat i + 2\hat j − \hat k$ and $ – \hat i + \hat j + \hat k$ respectively, in the ratio $2 : 1$ internally

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the position vector of the mid point of the vector joining the points $P(2, 3, 4)$ and $Q(4, 1, –2)$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the points A, B and C with position vectors, $ \overrightarrow a = 3\hat i − 4\hat j − 4\hat k, \overrightarrow b = 2\hat i − \hat j + \hat k$ and $ \overrightarrow c = \hat i − 3\hat j − 5\hat k$ , respectively form the vertices of a right angled triangle.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a$ and $ \overrightarrow b$ are two collinear vectors, then which of the following are incorrect:

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the angle between two vectors $ \overrightarrow a$ and $ \overrightarrow b$ with magnitudes $ \sqrt 3$ and $2$ , respectively having $ \overrightarrow a . \overrightarrow b = \sqrt 6.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

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

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the projection of the vector $ \hat i − \hat j$ on the vector $ \hat i + \hat j $.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the projection of the vector $ \hat i + 3\hat j + 7\hat k$ on the vector $7\hat i − \hat j + 8\hat k$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that each of the given three vectors is a unit vector: $ \large\frac{1}{7}$$ ( 2\hat i + 3\hat j + 6\hat k),\large\frac{1}{7}$$ ( 3\hat i - 6\hat j + 2\hat k), \large\frac{1}{7}$$ ( 6\hat i + 2\hat j - 3\hat k) $ Also, show that they are mutually perpendicular to each other.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find $| \overrightarrow a |$ and $| \overrightarrow b |$ , if $(\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a − \overrightarrow b) = 8$ and $| \overrightarrow a |= 8 | \overrightarrow b |.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Evaluate the product $(3\overrightarrow a − 5\overrightarrow b) ⋅ (2\overrightarrow a + 7\overrightarrow b)$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the magnitude of two vectors $ \overrightarrow a$ and $\overrightarrow b$ , having the same magnitude and such that the angle between them is $60^{\omicron}$ and their scalar product is $\large \frac{1}{2}$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find $| \overrightarrow x |$, if for a unit vector $\overrightarrow a , (\overrightarrow x − \overrightarrow a) ⋅ (\overrightarrow x + \overrightarrow a) =12$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = 2\hat i + 2\hat j + 3\hat k,\: \overrightarrow b = − \hat i + 2\hat j + \hat k$ and $ \overrightarrow c = 3\hat i + \hat j$ are such that $\overrightarrow a + λ\overrightarrow b $ is perpendicular to $ \overrightarrow c $ , then find the value of $λ.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that $| \overrightarrow a | \overrightarrow b + | \overrightarrow b | \overrightarrow a$ is perpendicular to $| \overrightarrow a | \overrightarrow b - | \overrightarrow b | \overrightarrow a$, for any two nonzero vectors $\overrightarrow a$ and $\overrightarrow b$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $ \overrightarrow a . \overrightarrow a = 0$ and $ \overrightarrow a . \overrightarrow b = 0$, then what can be concluded about the vector $\overrightarrow b$?

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If $ \overrightarrow a, \overrightarrow b, \overrightarrow c, $are unit vectors such that $ \overrightarrow a + \overrightarrow b + \overrightarrow c = \overrightarrow 0$, find the value of $ \overrightarrow a ⋅ \overrightarrow b + \overrightarrow b ⋅ \overrightarrow c + \overrightarrow c ⋅ \overrightarrow a$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If either vector $\overrightarrow a = \overrightarrow 0$ or $\overrightarrow b = \overrightarrow 0$, then $\overrightarrow a . \overrightarrow b = 0$. But the converse need not be true. Justify your answer with an example.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If the vertices $A, B, C$ of a triangle $ABC$ are $(1, 2, 3), (-1, 0, 0), (0, 1, 2)$ respectively, then find $ \angle ABC. \angle ABC$ is the angle between the vectors $ \overline {BA}$ and $\overline {BC}$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the vectors $2\hat i - \hat j + \hat k, \: \hat i - 3\hat j - 5\hat k$ and $3\hat i - 4\hat j - 4\hat k$ form the vertices of a right angled triangle.

asked Dec 6, 2012 by thanvigandhi_1

1 answer