If overrightarrow {rm A} = 2hat{i} + 3hat{j} - hat{k} and overrightarrow B =

English

Gujarati

Hindi

3-1.Vectors

medium

If $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ then projection of $\overrightarrow A $ on $\overrightarrow B $ will be

$\frac{3}{{\sqrt {13} }}$

$\frac{3}{{\sqrt {26} }}$

$\sqrt {\frac{3}{{26}}} $

$\sqrt {\frac{3}{{13}}} $

Solution

(b) $|\overrightarrow {\rm A} |\, = \,\sqrt {{2^2} + {3^2} + {{( – 1)}^2}} $$ = \sqrt {4 + 9 + 1} $ $ = \sqrt {14} $

$|\overrightarrow B |\, = \,\sqrt {{{( – 1)}^2} + {3^2} + {4^2}} $ $ = \sqrt {1 + 9 + 16} $ $ = \sqrt {26} $

$\overrightarrow A \,.\,\overrightarrow B = \,2\,( – 1) + 3 \times 3 + ( – 1)\,(4) = 3$

The projection of $\overrightarrow A \,\,{\rm{on}}\,\overrightarrow B $ $ = \frac{{\overrightarrow A \,.\,\overrightarrow B }}{{|\overrightarrow B |}}$ $ = \frac{3}{{\sqrt {26} }}$

Standard 11

Physics

If a vector $\vec A$ is parallel to another vector $\vec B$ then the resultant of the vector $\vec A \times \vec B$ will be equal to

medium

Show that the area of the triangle contained between the vectors $a$ and $b$ is one half of the magnitude of $a \times b .$

medium

Consider two vectors ${\overrightarrow F _1} = 2\hat i + 5\hat k$ and ${\overrightarrow F _2} = 3\hat j + 4\hat k.$ The magnitude of the scalar product of these vectors is

medium

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

medium

(AIIMS-2012)

If for two vectors $\overrightarrow A $ and $\overrightarrow B ,\overrightarrow A \times \overrightarrow B = 0,$ the vectors

medium

If $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ then projection of $\overrightarrow A $ on $\overrightarrow B $ will be

Solution

Similar Questions

If a vector $\vec A$ is parallel to another vector $\vec B$ then the resultant of the vector $\vec A \times \vec B$ will be equal to

Show that the area of the triangle contained between the vectors $a$ and $b$ is one half of the magnitude of $a \times b .$

Consider two vectors ${\overrightarrow F _1} = 2\hat i + 5\hat k$ and ${\overrightarrow F _2} = 3\hat j + 4\hat k.$ The magnitude of the scalar product of these vectors is

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

If for two vectors $\overrightarrow A $ and $\overrightarrow B ,\overrightarrow A \times \overrightarrow B = 0,$ the vectors

Start a Free Trial Now