Linear Depend...

Linear Dependence and Independence of Vectors

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Q. System of vectors

a_{1}, a_{2}, . . . . . . . a_{n}

is said to be linearly dependent if there exists a system of scalars

(c_{1}, c_{2} - - - c_{n} s u c h t h a t c_{1} ¯ a + c_{2}_{2} + . . . c_{n}_{n} = ¯ 0

True
False

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If the vectors $\to a$ and $\to b$ are perpendicular to each other, then a vector $\to v$ in terms of $\to a$ and $\to b$ satisfying the equations
$\to v . \to a = 0, \to v . \to b = 1 a n d [\to v \to a \to b] = 1$ is

None of these
$\frac{\to b}{| \to b |^{2}} + \frac{\to a \times \to b}{| \to a \times \to b |^{2}}$
$\frac{\to b}{| \to b |} + \frac{\to a \times \to b}{| \to a \times \to b |^{2}}$
$\frac{\to b}{| \to b |^{2}} + \frac{\to a \times \to b}{| \to a \times \to b |}$