If a - b - c - are non-coplanar vectors- prove that the following vectors are non-coplanar-i 2 a - b -3 c - a - b -2 c - and a - b -3 c -ii a -2 b -3 c - 2 a -b -3 c - and a -b -c -

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Integration of Irrational Algebraic Fractions - 1

If a →, b →, ...

Question

If $\vec{a}$ , $\vec{b}$ , $\vec{c}$ are non-coplanar vectors, prove that the following vectors are non-coplanar:
(i) $2 \vec{a} - \vec{b} + 3 \vec{c}, \vec{a} + \vec{b} - 2 \vec{c} and \vec{a} + \vec{b} - 3 \vec{c}$

(ii) $\vec{a} + 2 \vec{b} + 3 \vec{c}, 2 \vec{a} + \vec{b} + 3 \vec{c} and \vec{a} + \vec{b} + \vec{c}$

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¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

3 ¯ ¯ ¯ a - 2 ¯ ¯ b - 4 ¯ ¯ c

- ¯ ¯ ¯ a + 2 ¯ ¯ c

- 2 ¯ ¯ ¯ a + ¯ ¯ b + 3 ¯ ¯ c

\vec{a}

\vec{b}

\vec{c}

5 \vec{a} + 6 \vec{b} + 7 \vec{c,} 7 \vec{a} - 8 \vec{b} + 9 \vec{c} and 3 \vec{a} + 20 \vec{b} + 5 \vec{c}

\vec{a} - 2 \vec{b} + 3 \vec{c}, - 3 \vec{b} + 5 \vec{c} and - 2 \vec{a} + 3 \vec{b} - 4 \vec{c}

\to a, \to b a n d \to c

\to a - 2 \to b + 3 c, - - \to 2 a + \to 3 b - \to 4 c a n d - \to b + \to 2 c

2 \to a - \to b + 3 \to c, \to a - 2 \to b + λ \to c

μ \to a - 5 \to b

\to a, \to b, \to c

2 \to a + 3 \to b - \to c, \to a - 2 \to b + 3 \to c, 3 \to a + 4 \to b - 2 \to c a n d \to a - 6 \to b + 6 \to c

\to a, \to b a n d \to c

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