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Three vectors...

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Three vectors A, B andC add up to zero. Findwhich is false.(a)(AX B)XC is not zero unless B, C are parallel.(b)(Ax B) C is not zero unless B, C are parallel.(c) If A, B, C define a plane, (Ax B)xC is inthat plane.(d) (AxB)-C= AB\vert C-c A2 + B2

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a

b

c

are three non-zero vectors such that

a . | b \times c | = 0

b

c

are not parallel then

a

b

c

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

are three non-zero vectors and

¯ ¯ ¯ a \neq ¯ ¯ b

¯ ¯ ¯ a \times ¯ ¯ c = ¯ ¯ b \times ¯ ¯ c

Q. Three vectors

A, B

C

add up to zero. Find which is false

a, b, c

are three non coplanar, non zero vectors, then

(a . a) b \times c + (a . b) c \times a + (a . c) a \times b

\vec{a}, \vec{b}, \vec{c}

are three non-zero vectors, no two of which are collinear and the vector

\vec{a} + \vec{b}

is collinear with

\vec{c}, \vec{b} + \vec{c}

is collinear with

\vec{a},

\vec{a} + \vec{b} + \vec{c} =

\vec{a}

\vec{b}

\vec{c}

(d) none of these

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