If a and b are two non zero vectors such that a-b - b-a- then

Given, a×b = b×a a×b = (a×b) ⇒ 2(a×b) = 0 ⇒ (a×b) = 0 Hence, a is parallel to b a = kb, where k is a scalar quantity ...

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Standard XII

Mathematics

Linear Combination of Vectors

If a and b ar...

Question

If $\to a$ and $\to b$ are two non zero vectors such that $\to a \times \to b = \to b \times \to a,$ then

\to a \cdot \to b = 0

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\to a = k \to b,

where

k

is a scalar quantity

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\to a

and

\to b

are always unlike vectors

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\to a

and

\to b

are always equal vectors

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Solution

The correct option is B $\to a = k \to b,$ where $k$ is a scalar quantity
Given,
$\to a \times \to b = \to b \times \to a$
$\to a \times \to b = - (\to a \times \to b)$
$\Rightarrow 2 (\to a \times \to b) = 0$
$\Rightarrow (\to a \times \to b) = 0$
Hence, $\to a$ is parallel to $\to b$
$\to a = k \to b$ , where $k$ is a scalar quantity

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Similar questions

Q. If

\to a, \to b, \to c, \to d

are non-zero vectors, then

[\to a \times \to b \to a \times \to c \to d]

can be simplified as:

Q. For any three vectors

\to a, \to b

and

\to c

, prove that vectors

\to a - \to b, \to b - \to c

and

\to c - \to a

are coplanar.

Q. If

\to a, \to b, \to c, \to d

are non-zero vectors satisfying

\to a = \to b + \to c

\to b \times \to d = \to 0

and

\to c \cdot \to d = 0

, then

\frac{\to d \times (\to a \times \to d)}{| \to d |^{2}}

is always equal to

Q. Let

\to a, \to b, \to c

be non-coplanar vectors and

\to d

be a non-zero vector which is perpendicular to

\to a + \to b + \to c

. If

\to d = x \to b \times \to c + y \to c \times \to a + z \to a \times \to b

then

Q. If

\to a, \to b, \to c

are non - coplanar vectors, then

\frac{a . (b \times c)}{(c \times a) . b} + \frac{b . (a \times c)}{c . (a \times b)} = ?

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Linear Combination of Vectors

Standard XII Mathematics

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If →a and →b are two non zero vectors such that →a×→b=→b×→a, then

The correct option is B →a=k→b, where k is a scalar quantityGiven, →a×→b=→b×→a →a×→b=−(→a×→b) ⇒2(→a×→b)=0 ⇒(→a×→b)=0 Hence, →a is parallel to →b →a=k→b, where k is a scalar quantity

If $\to a$ and $\to b$ are two non zero vectors such that $\to a \times \to b = \to b \times \to a,$ then