Vectors $\to a =^i + 2^j + 3^k, \to b = 2^i -^j +^k$ and $\to c = 3^i +^j + 4^k$ are so placed that the end point of one vector is the starting point of the next vector, then the vectors are

Not coplanar

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Coplanar but cannot form a triangle

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Coplanar and form a triangle

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Coplanar and can form a right-angled triangle

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Solution

The correct option is C Coplanar and form a triangle
Given $\to A B = \to a =^i + 2^j + 3^k$
$\to B C = \to b = 2^i -^j +^k$
$\to A C = \to c = 3^i +^j + 4^k$
To check coplanar $[\to a \to b \to c] = 0$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 2 & - 1 & 1 3 & 1 & 4 \end{matrix} ∣ ∣ ∣ ∣$ =0
$1 (- 5) - 2 (5) + 3 (5) = 0$
It is coplanar
Now to check a triangular
$\to A C = \to A B + \to B C$
$^i + 2^j + 3^k + 2^i -^j +^k = \to A C$
$3^i +^j + 4^k = 3^i +^j + 4^k = \to A C$
So condition is followed it is triangular

Suggest Corrections

Similar questions

\to a =^i + 2^j + 3^k; ¯ b = 2^i -^j +^k

\to c = 3^i +^j + 4^k

^i + 2^j + 3^k

2^i -^j +^k

3^i +^j + 4^k

\to a = 3^i - 2^j +^k, \to b =^i - 3^j + 5^k a n d \to c = 2^i +^j - 4^k

\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k

\to C = 2^i -^j + 4^k

\to a = (3^i - 4^j - 4^k)

\to b = (2^i -^j +^k)

\to c = (^i - 3^j - 5^k)

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