Let - b- - are three unit vectors such that -b- is also a unit vector- If pairwise angles between - b- - are -1- -2 and -3 respectively then cos-1-cos-2-cos-3 equals-

Let $^a,^b a n d^c$ be three unit vectors such that
$^a \times (^b \times^c) = \frac{\sqrt{3}}{2} (^b +^c) .$ If
$^b$ is not parallel to $^c$ , then the angle between $^a$ and $^b$ is

Q. If

^a,^b,^c

are unit vectors such that

^a .^b = 0 =^a .^c

and the angle between

^b

and

^c

π / 3

, then the value of

∣ ∣^a \times^b -^a \times^c ∣ ∣

Q. If three unit vector

^a,^b,^c

satisfy

^a +^b +^c =^0

, then the angle between

^a

and

^b

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Let ^a,^b,^c are three unit vectors such that ^a+^b+^c is also a unit vector. If pairwise angles between ^a,^b,^c are θ1,θ2 and θ3 respectively then cosθ1+cosθ2+cosθ3 equals?

The correct option is D −1∣∣^a+^b+^c∣∣=1 ⇒|a|+|b|+|c|+2(^a−^b+^b−^c+^c^a)=1 =3+2(cosθ1+cosθ2+cosθ3)=1 cosθ1+cosθ2+cosθ3=−1

Let $^a,^b,^c$ are three unit vectors such that $^a +^b +^c$ is also a unit vector. If pairwise angles between $^a,^b,^c$ are $θ_{1}, θ_{2}$ and $θ_{3}$ respectively then $cos θ_{1} + cos θ_{2} + cos θ_{3}$ equals?

The correct option is D $- 1$
$∣ ∣^a +^b +^c ∣ ∣ = 1$

$\Rightarrow | a | + | b | + | c | + 2 (^a -^b +^b -^c +^c^a) = 1$

$= 3 + 2 (cos θ_{1} + cos θ_{2} + cos θ_{3}) = 1$

$cos θ_{1} + cos θ_{2} + cos θ_{3} = - 1$