Let a- b- c are vectors such that -a-2-b-3-c-3 and 3a-2b is perpendicular to c- 3b-2c is perpendicular to a and 3c-2a is perpendicular to b- Then the value of -a-b-c-

Given : (3a 2b)·c=0 ⇒ 3a·c 2b·c=0⋯(i), (3b 2c)·a=0 ⇒ 3a·b 2a·c=0⋯(ii) nbsp; and nbsp; (3c 2a)·b=0 ⇒ 3b·c 2a·b=0⋯(iii) Adding (i),(ii) and (iii): nbsp; we ...

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Standard XII

Mathematics

Cross Product of Two Vectors

Let a, b, c a...

Question

Let $\to a, \to b, \to c$ are vectors such that $| \to a | = 2, | \to b | = 3, | \to c | = \sqrt{3}$ and $(3 \to a - 2 \to b)$ is perpendicular to $\to c, (3 \to b - 2 \to c)$ is perpendicular to $\to a$ and $(3 \to c - 2 \to a)$ is perpendicular to $\to b .$ Then the value of $| \to a + \to b + \to c | =$

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Solution

Given :
$(3 \to a - 2 \to b) \cdot \to c = 0 \Rightarrow 3 \to a \cdot \to c - 2 \to b \cdot \to c = 0 \dots (i)$ ,
$(3 \to b - 2 \to c) \cdot \to a = 0 \Rightarrow 3 \to a \cdot \to b - 2 \to a \cdot \to c = 0 \dots (i i)$
and
$(3 \to c - 2 \to a) \cdot \to b = 0 \Rightarrow 3 \to b \cdot \to c - 2 \to a \cdot \to b = 0 \dots (i i i)$
Adding $(i), (i i)$ and $(i i i) :$
we get, $(\to a \cdot \to b + \to b \cdot \to c + \to a \cdot \to c) = 0 \dots (A)$
Also,
$| \to a + \to b + \to c |^{2} = | \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 2 (\to a \cdot \to b + \to b \cdot \to c + \to a \cdot \to c) = 4 + 9 + 3 [using (A)] [∵ | \to a | = 2, | \to b | = 3, | \to c | = \sqrt{3}] = 16 \Rightarrow | \to a + \to b + \to c | = 4$

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Cross Product of Two Vectors

Standard XII Mathematics

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Let →a,→b,→c are vectors such that |→a|=2,|→b|=3,|→c|=√3 and (3→a−2→b) is perpendicular to →c,(3→b−2→c) is perpendicular to →a and (3→c−2→a) is perpendicular to →b. Then the value of |→a+→b+→c|=