Let a- b- c- are three unit vectors such that no two of the vectors are collinear- If the vector a-b- is collinear with c- and the vector b-c- is collinear with a- then the value of - a - b - c - is

A+b= xc b+c= ya Now, a+b+ c=(1+x)c ⋯(1) and a+b+c=(1+y)a ⋯(2) From (1) (2) (1+x)c (1+y)a=0 ⇒ mc na=0 From here c,a are collinear but as per the question ...

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Standard XII

Mathematics

Test for Collinearity of Vectors

Let a⃗, b⃗, c...

Question

Let $\to a, \to b, \to c$ are three unit vectors such that no two of the vectors are collinear. If the vector $\to a + \to b$ is collinear with $\to c$ and the vector $\to b + \to c$ is collinear with $\to a,$ then the value of $| \to a + \to b + \to c |$ is

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Solution

$\to a + \to b = x \to c$
$\to b + \to c = y \to a$
Now, $\to a + \to b + \to c = (1 + x) \to c \dots (1)$
and $\to a + \to b + \to c = (1 + y) \to a \dots (2)$
From $(1) - (2)$
$(1 + x) \to c - (1 + y) \to a = 0$
$\Rightarrow m \to c - n \to a = 0$
From here $\to c, \to a$ are collinear but as per the question $\to c, \to a$ are non-collinear.
$∴ x = - 1; y = - 1$
$∴ | \to a + \to b + \to c | = 0$

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Test for Collinearity of Vectors

Standard XII Mathematics

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Let →a,→b,→c are three unit vectors such that no two of the vectors are collinear. If the vector →a+→b is collinear with →c and the vector →b+→c is collinear with →a, then the value of |→a+→b+→c| is

→a+→b=x→c →b+→c=y→a Now, →a+→b+→c=(1+x)→c ⋯(1) and →a+→b+→c=(1+y)→a ⋯(2) From (1)−(2) (1+x)→c−(1+y)→a=0 ⇒m→c−n→a=0 From here →c,→a are collinear but as per the question →c,→a are non-collinear. ∴x=−1; y=−1 ∴|→a+→b+→c|=0

Let $\to a, \to b, \to c$ are three unit vectors such that no two of the vectors are collinear. If the vector $\to a + \to b$ is collinear with $\to c$ and the vector $\to b + \to c$ is collinear with $\to a,$ then the value of $| \to a + \to b + \to c |$ is