I- If a- b- are two unit vectors a- b- Then -a-b- is maximum when - is maximumII- If a- b- are two unit vectors -a-b- is maximum when - is minimum

The correct option is C Both I and II are true |a⃗× #160;b⃗| = |a||b| sinθ #160;and #160; |a⃗·b⃗| = |a||b| cosθ We know that sine is an increasi ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

I. If a⃗, b...

Question

I. If $\to a, \to b$ are two unit vectors $(\to a, \to b) = θ$ . Then $| \to a \times \to b |$ is maximum when $θ$ is maximum
II. If $\to a, \to b$ are two unit vectors $| \to a \times \to b |$ is maximum when $θ$ is minimum

Only I is true

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Only II is true

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Both I and II are true

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Neither l nor ll are true

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Solution

The correct option is C Both I and II are true
$| \to a \times \to b | = | a | | b | sin θ$ and $| \to a \cdot \to b | = | a | | b | cos θ$
We know that sine is an increasing function of $θ$ in the range $[0, 90^{o}]$ and cosine is a decreasing function.
Hence both the above statements are true.

Suggest Corrections

Similar questions

Q. I : If

| \to a + \to b | = | \to a - \to b |

, then

(\to a, \to b) = \frac{π}{2}

.
II : If

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

are unit vectors, then

(\to a, \to b) = \frac{2 π}{3}

Q. If

\to a

and

\to b

are unequal vectors such that

(\to a - \to b) \times [(\to b + \to a) \times (2 \to a + \to b)] = \to a + \to b

, then the angle

θ

between

\to a

and

\to b

Q. If

\to a

and

\to b

are two unit vectors inclined at an angle

θ

such that

\to a + \to b

is a unit vector, then

θ

is equal to

Q. If

\to a

and

\to b

are two unit vector and

θ

is the angle between them, then

(\to a + \to b)

is a unit vector if

θ =

\to A

and

\to B

are two vectors and

θ

is the angle between them, if

| \to A \times \to B | = \sqrt{3} (\to A \cdot \to B)

the value of

θ

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I. If →a,→b are two unit vectors (→a,→b)=θ. Then |→a×→b| is maximum when θ is maximumII. If →a,→b are two unit vectors |→a×→b| is maximum when θ is minimum

The correct option is C Both I and II are true|→a×→b|=|a||b|sinθ and |→a⋅→b|=|a||b|cosθWe know that sine is an increasing function of θ in the range [0,90o] and cosine is a decreasing function.Hence both the above statements are true.

I. If $\to a, \to b$ are two unit vectors $(\to a, \to b) = θ$ . Then $| \to a \times \to b |$ is maximum when $θ$ is maximum
II. If $\to a, \to b$ are two unit vectors $| \to a \times \to b |$ is maximum when $θ$ is minimum

The correct option is C Both I and II are true
$| \to a \times \to b | = | a | | b | sin θ$ and $| \to a \cdot \to b | = | a | | b | cos θ$
We know that sine is an increasing function of $θ$ in the range $[0, 90^{o}]$ and cosine is a decreasing function.
Hence both the above statements are true.