Given three vectors a- b- c- each two of which are non collinear Equally Separated- Further if a-b- is collinear with c- b-c- is collinear with a- - a- - - b- - - c- -2 then the value of a-b-b-c-c-a-

The correct option is B is 3 As per #160;the given condition, the vector a , b & c #160; are equally separated with 120 ^ o betwee ...

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Standard XII

Mathematics

Equation of Tangent at a Point (x,y) in Terms of f'(x)

Given three v...

Question

Given three vectors $\to a, \to b$ & $\to c$ , each two of which are non collinear (Equally Separated). Further if $(\to a + \to b)$ is collinear with $\to c, (\to b + \to c)$ is collinear with $\to a$ & $| \to a | = ∣ ∣ \to b ∣ ∣ = | \to c | = \sqrt{2}$ then the value of $\to a . \to b + \to b . \to c + \to c . \to a$ :

3

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0

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Solution

The correct option is B is $- 3$
As per the given condition, the vector $\to a, \to b & \to c$ are equally separated with $120^{o}$ between them

So, $\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a = a b cos 120^{o} + b c cos 120^{o} + c a cos 120^{o}$

$= 3 \times \sqrt{2} \times \sqrt{2} (\frac{- 1}{2})$

$= 3 \times 2 \times (\frac{- 1}{2}) = - 3$

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Given three vectors →a,→b & →c, each two of which are non collinear (Equally Separated). Further if (→a+→b) is collinear with →c,(→b+→c) is collinear with →a & |→a|=∣∣→b∣∣=|→c|=√2 then the value of →a.→b+→b.→c+→c.→a:

The correct option is B is −3As per the given condition, the vector →a,→b&→c are equally separated with 120o between themSo, →a⋅→b+→b⋅→c+→c⋅→a=abcos120o+bccos120o+cacos120o =3×√2×√2(−12) =3×2×(−12)=−3