For non-zero vectors a- and b- if -a-b-a-b- then a- and b- are

The correct option is B inclined at an obtuse angleLet the angle between a and b is α |a+b| lt;|a b| Squaring both side ⇒ |a|^2+|b|^2+2|a||b|cosα lt;|a|^2+ ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Parallel

For non-zero ...

Question

For non-zero vectors $\to a$ and $\to b$ if $| \to a + \to b | < | \to a - \to b |$ , then $\to a$ and $\to b$ are

collinear

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perpendicular to each other

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inclined at an acute angle

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inclined at an obtuse angle

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Solution

The correct option is D inclined at an obtuse angle
Let the angle between $\to a$ and $\to b$ is $α$
$| \to a + \to b | < | \to a - \to b |$
Squaring both side
$\Rightarrow | \to a |^{2} + | \to b |^{2} + 2 | \to a | | \to b | cos α < | \to a |^{2} + | \to b |^{2} - 2 | \to a | | \to b | cos α$
$\Rightarrow | \to a | | \to b | cos α < 0$
$\Rightarrow cos α < 0$

Thus $α$ is an obtuse angle.

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Similar questions

Q. For any three vectors

\to a, \to b

and

\to c

, prove that

[\to a + \to b, \to b + \to c, \to c + \to a] = 2 [\to a \to b \to c]

. Hence prove that the vectors

\to a + \to b, \to b + \to c, \to c + \to a

are coplanar. If and only if

\to a, \to b, \to c

are coplanar.

Q. If

\to a, \to b, \to c

are non-caplanar non-zero vectors and

\to r

is any vector in space then

[\to b \to c \to r] \to a + [\to c \to a \to r] \to b + [\to a \to b \to r] \to c

is equal to

Q. If

\to a, \to b, \to c

are non-coplanar vectors and

λ

is a real number, then the vectors

\to a + 2 \to b + 3 \to c, λ \to b + 4 \to c

and

(2 λ - 1) \to c

are non-coplanar for

Q. If

\to a, \to b, \to c

are non-coplanar vector and

\to d = λ \to a + μ \to b + ν \to c,

then

λ

is equal to -

\to a, \to b, \to c

are three non coplanar non zero vectors and

\to r

is any vector in space, then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

is equal to

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For non-zero vectors →a and →b if |→a+→b|<|→a−→b|, then →a and →b are

The correct option is D inclined at an obtuse angleLet the angle between →a and →b is α |→a+→b|<|→a−→b| Squaring both side ⇒|→a|2+|→b|2+2|→a||→b|cosα<|→a|2+|→b|2−2|→a||→b|cosα ⇒|→a||→b|cosα<0 ⇒cosα<0 Thus α is an obtuse angle.

For non-zero vectors $\to a$ and $\to b$ if $| \to a + \to b | < | \to a - \to b |$ , then $\to a$ and $\to b$ are