Let the unit vectors a- and b- are perpendicular and the unimodulus vector c- inclined at an angle - to a- and b- If c-l a-m b-na-b- then

The correct options are A l=m B n^2 =1 2l^2 C n^2= cos 2 α D m^2 =1+cos 2 α/2 |a⃗|=|b⃗|=|c⃗|=1 Angle between b⃗ and c⃗= angle between a⃗ and c⃗ ⇒b⃗.c⃗=a⃗.c⃗= ...

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Byju's Answer

Standard XII

Mathematics

Direction Cosines

Let the unit ...

Question

Let the unit vectors $\to a$ and $\to b$ are perpendicular and the unimodulus vector $\to c$ inclined at an angle $α$ to $\to a$ and $\to b$ . If $\to c = l \to a + m \to b + n (\to a \times \to b)$ , then

l=m

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$n^{2} = 1 - 2 l^{2}$

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$n^{2} = - c o s 2 α$

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$m^{2} = \frac{1 + c o s 2 α}{2}$

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Solution

The correct options are
A
l=m

B
$n^{2} = 1 - 2 l^{2}$

C
$n^{2} = - c o s 2 α$

D
$m^{2} = \frac{1 + c o s 2 α}{2}$

$| \to a | = | \to b | = | \to c | = 1$
Angle between $\to b$ and $\to c$ = angle between $\to a$ and $\to c$
$\Rightarrow \to b . \to c = \to a . \to c = c o s α$
Also $\to a ⊥ \to b \Rightarrow \to a . \to b = 0$
$\to c = l \to a + m \to b + n (\to a \times \to b) \to a . \to c = l = c o s α . \to b . \to c = m = c o s α \Rightarrow m = l = c o s α \Rightarrow 1 = 2 l^{2} + n^{2} \Rightarrow n^{2} = 1 - 2 l^{2} = 1 - 2 c o s^{2} α = - c o s 2 α \Rightarrow l^{2} = m^{2} = \frac{1 - n^{2}}{2} = \frac{1 + c o s 2 α}{2}$

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Similar questions

Q. Let the unit vectors

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and

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Let the unit vectors →a and →b are perpendicular and the unimodulus vector →c inclined at an angle α to →a and →b. If →c=l→a+m→b+n(→a×→b), then

Let the unit vectors $\to a$ and $\to b$ are perpendicular and the unimodulus vector $\to c$ inclined at an angle $α$ to $\to a$ and $\to b$ . If $\to c = l \to a + m \to b + n (\to a \times \to b)$ , then