Magnitudes of vectors a- b- c- are 3-4-5 respectively- If a- and b-c- b- and c-a- c- and a-b- are mutually perpendicular- then the magnitude of a-b-c- is-A- 4 -2- 3 -2- 5 -2D- 3 -3

The correct option is C 5√(2)a·(b+c)=0 ⇒a·b+a·c=0 Similarly, b·c+b·a=0 c·a+c·b =0 Adding these 2(a·b+b·c+c·a)=0 Now |a+b+c|^2=|a|^2+|b|^2+|c|^2+2(a·b+b·c+c ...

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Standard XII

Physics

Comparing Vectors

Magnitudes of...

Question

Magnitudes of vectors $\to a, \to b, \to c$ are $3, 4, 5$ respectively. If $\to a$ and $\to b + \to c$ , $\to b$ and $\to c + \to a$ , $\to c$ and $\to a + \to b$ are mutually perpendicular, then the magnitude of $\to a + \to b + \to c$ is,

4 \sqrt{2}

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3 \sqrt{2}

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5 \sqrt{2}

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3 \sqrt{3}

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Solution

The correct option is C $5 \sqrt{2}$
$\to a \cdot (\to b + \to c) = 0 \Rightarrow \to a \cdot \to b + \to a \cdot \to c = 0$

Similarly, $\to b \cdot \to c + \to b \cdot \to a = 0$

$\to c \cdot \to a + \to c \cdot \to b = 0$

Adding these $2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a) = 0$

Now $| \to a + \to b + \to c |^{2} = | \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a)$

$= 9 + 16 + 25 = 50$

$| \to a + \to b + \to c | = 5 \sqrt{2}$

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Magnitudes of vectors →a,→b,→c are 3,4,5 respectively. If →a and →b+→c, →b and →c+→a, →c and →a+→b are mutually perpendicular, then the magnitude of →a+→b+→c is,

Magnitudes of vectors $\to a, \to b, \to c$ are $3, 4, 5$ respectively. If $\to a$ and $\to b + \to c$ , $\to b$ and $\to c + \to a$ , $\to c$ and $\to a + \to b$ are mutually perpendicular, then the magnitude of $\to a + \to b + \to c$ is,