Given three vectors a-6-3- b-2-6- and c-2-21- such that -a-b-c-Then the resolution of the vector - into components with respect to a and b is given by

If $\to a$ and $\to b$ are vectors such that $| \to a + \to b | = \sqrt{29}$ and $\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b,$ then a possible value of $(\to a + \to b) . (- 7^i + 2^j + 3^k)$ is

Q. If

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

are non-coplanar vectors, then show that the vectors

- ¯ ¯ ¯ a + 3 ¯ ¯ b - 5 ¯ ¯ c, - ¯ ¯ ¯ a + ¯ ¯ b + ¯ ¯ c

and

2 ¯ ¯ ¯ a - 3 ¯ ¯ b + ¯ ¯ c

are coplanar

Q. Four points given by position vectors

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

are coplanar, where

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

are non-coplanar vectors.

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Given three vectors →a=6^i−3^j →b=2^i−6^j and →c=−2^i+21^j such that →α=→a+→b+→c.Then the resolution of the vector →α into components with respect to →a and →b is given by

The correct option is B 2→a−3→b→α=→a+→b+→c=6^i+12^jLet →α=x→a+y→b⇒6x+2y=6−3x−6y=12∴x=2,y=−3∴→α=2→a−3→b

Given three vectors $\to a = 6^i - 3^j$ $\to b = 2^i - 6^j$ and $\to c = - 2^i + 21^j$ such that $\to α = \to a + \to b + \to c .$ Then the resolution of the vector $\to α$ into components with respect to $\to a$ and $\to b$ is given by

The correct option is B $2 \to a - 3 \to b$
$\to α = \to a + \to b + \to c$
$= 6^i + 12^j$
Let $\to α = x \to a + y \to b$ $\Rightarrow 6 x + 2 y = 6$
$- 3 x - 6 y = 12$
$∴ x = 2, y = - 3$
$∴ \to α = 2 \to a - 3 \to b$