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 ∣ ∣

Join BYJU'S Learning Program

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 −1Let ^a+^b=→x|^a+^b+^c|=√x2+c2+2→x.^c=√a2+b2+2ab(cosθ1)+c2+2bc(cosθ2)+2ac(cosθ3)=1 as given.⇒1=1+1+1+2(cosθ1+cosθ2+cosθ3)⇒(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