If for two vector overrightarrow A and overrightarrow B , sum (overrightarrow A + overrightarrow B )

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3-1.Vectors

hard

If for two vector $\overrightarrow A $ and $\overrightarrow B $, sum $(\overrightarrow A + \overrightarrow B )$ is perpendicular to the difference $(\overrightarrow A - \overrightarrow B )$. The ratio of their magnitude is

$1$

$2$

$3$

None of these

Solution

(a) $(\overrightarrow A + \overrightarrow B )$ is perpendicular to $(\overrightarrow A – \overrightarrow B )$. Thus

$(\overrightarrow A + \overrightarrow B )$.$(\overrightarrow A – \overrightarrow B ) = 0$
or ${A^2} + \overrightarrow B \,.\,\overrightarrow A – \overrightarrow A \,.\,\overrightarrow B – {B^2} = 0\,$
Because of commutative property of dot product

$\overrightarrow A .\overrightarrow B = \overrightarrow B .\overrightarrow A $

$\therefore $${A^2} – {B^2} = 0$ or $A = B$

Thus the ratio of magnitudes $A/B = 1$

Standard 11

Physics

The two vectors $\vec A$ and $\vec B$ that are parallel to each other are

medium

For any two vectors $\overrightarrow A $ and $\overrightarrow B $, if $\overrightarrow A \,.\,\overrightarrow B = \,\,|\overrightarrow A \times \overrightarrow B |,$ the magnitude of $\overrightarrow C = \overrightarrow A + \overrightarrow B $ is equal to

easy

If $|\overrightarrow A \times \overrightarrow B |\, = \,|\overrightarrow A \,.\,\overrightarrow B |,$ then angle between $\overrightarrow A $ and $\overrightarrow B $ will be …….. $^o$

medium

(AIIMS-2000)

${\vec A }$, ${\vec B }$ and ${\vec C }$ are three non-collinear, non co-planar vectors. What can you say about directin of $\vec A \, \times \,\left( {\vec B \, \times \vec {\,C} } \right)$ ?

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

If for two vector $\overrightarrow A $ and $\overrightarrow B $, sum $(\overrightarrow A + \overrightarrow B )$ is perpendicular to the difference $(\overrightarrow A - \overrightarrow B )$. The ratio of their magnitude is

Solution

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