Recent questions tagged p448

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

If $\overrightarrow a$ is a nonzero vector of magnitude $" a "$ and $λ$ a nonzero scalar, then $λ \overrightarrow a$ is unit vector if

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Ask Questions, Get Answers

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

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

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 $\large \frac{1}{2}$.

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

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 $λ.$

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 $\overrightarrow b$.

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

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.

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 $\overline {BC}$.

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

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.

If $\overrightarrow a$ is a nonzero vector of magnitude $" a "$ and $λ$ a nonzero scalar, then $λ \overrightarrow a$ is unit vector if