I - If -a-b-a-b- then a- b- -2-II - If a-b- a-b- are unit vectors- then a-b- -2-3-

The correct option is C Both I amp; II are trueI. |a + #160;b| = |a #160;b|, ⇒ a^2 + b^2 + #160; #160;2|a||b|cosθ = #160;a^2 + b^2 2|a| ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios Using Right Angled Triangle

I : If |a⃗+...

Question

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 $(\to a, \to b) = \frac{2 π}{3}$ .

Only I is true

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Only II is true

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Both I & II are true

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Neither I nor II are true

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Solution

The correct option is C Both I & II are true
I. $| ¯ ¯ ¯ a + ¯ ¯ b | = | ¯ ¯ ¯ a - ¯ ¯ b |, \Rightarrow a^{2} + b^{2} + 2 | ¯ ¯ ¯ a | | ¯ ¯ b | cos θ = a^{2} + b^{2} - 2 | ¯ ¯ ¯ a | | ¯ ¯ b | cos θ$
$\Rightarrow cos θ = 0$ , i.e. $θ = \frac{π}{2}$
II. $| ¯ ¯ ¯ a + ¯ ¯ b |^{2} = 1$
$\Rightarrow a^{2} + b^{2} + 2 ¯ ¯ ¯ a . ¯ ¯ b = 1$
$\Rightarrow cos θ = \frac{- 1}{2}$
$\Rightarrow θ = \frac{2 π}{3}$

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Similar questions

Q. Assertion :Statement-I : The angle between vectors

\to A \times \to B

and

\to B \times \to A

π

radian.
Because Reason: Statement-II :

\to B \times \to A = - \to A \times \to B

Q. 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

Q. If

\to a, \to b, \to c

are unit vectors such that

\to a + \to b + \to c = \to 0

and

(\to a, \to b) = \frac{π}{3}

, then

∣ ∣ \to a \times \to b ∣ ∣ + ∣ ∣ \to b \times \to c ∣ ∣ + | \to c \times \to a | =

Q. Statement-I :

\to a \times (\to b \times \to c), \to b \times (\to c \times \to a), \to c \times (\to a \times \to b)

are coplanar vectors.

Statement-II: If there exists scalars

l, m, n

not all zero such that

l \to a + m \to b + n \to c = \to 0

, then the vectors

\to a, \to b, \to c

are coplanar

Q. If

\to a, \to b, \to c

are unit vectors such that

\to a + \to b + \to c = \to 0

and

(\to a, \to b) = \frac{π}{3}

then

| \to a \times \to b | + | \to b \times \to c | + | \to c \times \to a | =

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I : If |→a+→b|=|→a−→b|, then (→a,→b)=π2.II : If →a,→b,→a+→b are unit vectors, then (→a,→b)=2π3.

The correct option is C Both I & II are trueI. |¯¯¯a+¯¯b|=|¯¯¯a−¯¯b|,⇒a2+b2+2|¯¯¯a||¯¯b|cosθ=a2+b2−2|¯¯¯a||¯¯b|cosθ ⇒cosθ=0, i.e. θ=π2II. |¯¯¯a+¯¯b|2=1 ⇒a2+b2+2¯¯¯a.¯¯b=1 ⇒cosθ=−12 ⇒θ=2π3

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 $(\to a, \to b) = \frac{2 π}{3}$ .