If a- is a vector and x is a non-zero scalar then

The correct option is A xa⃗ is a vector collinear to a⃗ x a is a vector in the direction of a #160; if x gt;0 x a is a ve ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

If a⃗ is a ...

Question

If $\to a$ is a vector and $x$ is a non-zero scalar then

x \to a

is a vector in the direction of

\to a

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x \to a

is a vector collinear to

\to a

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x \to a

and

\to a

have independent directions

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None of these

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Solution

The correct option is A $x \to a$ is a vector collinear to $\to a$
$x \to a$ is a vector in the direction of $\to a$ if $x > 0$
$x \to a$ is a vector opposite to the direction of $\to a$ if $x < 0$
$∴$ $x \to a$ is a vector collinear to $\to a$
Hence, option B.

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Similar questions

Q. If

\to a

is a vector and

x

is a non-zero scalar, then -

Q. Any vector

\to r

in the plane of two non-zero, non collinear vectors

\to a

and

\to b

can be expressed uniquely as a linear combination

x \to a + y \to b

\to a a n d \to b,

where

x \to a a n d y \to b

are the components of vector

\to r

Q. Let

\to a, \to b, \to c

be unit vectors such that

\to a ⊥ \to b

and

\to c

is equally inclined to

\to a

and

\to b

. If

\to c = x \to a + y \to b + z (\to a \times \to b)

, then

Q. Any vector

\to r

in the plane of two non-zero, non collinear vectors

\to a

and

\to b

can be expressed uniquely as a linear combination

x \to a + y \to b

\to a a n d \to b,

where

x \to a a n d y \to b

are the components of vector

\to r

Q. Assertion :Vectors

\to a, \to b, \to c

are coplanar. Reason:

(x \to a + y \to b) = \to 0 \Rightarrow

x = 0 and y = 0.

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If →a is a vector and x is a non-zero scalar then

The correct option is A x→a is a vector collinear to →ax→a is a vector in the direction of →a if x>0x→a is a vector opposite to the direction of →a if x<0∴ x→a is a vector collinear to →aHence, option B.

If $\to a$ is a vector and $x$ is a non-zero scalar then

The correct option is A $x \to a$ is a vector collinear to $\to a$
$x \to a$ is a vector in the direction of $\to a$ if $x > 0$
$x \to a$ is a vector opposite to the direction of $\to a$ if $x < 0$
$∴$ $x \to a$ is a vector collinear to $\to a$
Hence, option B.