The vectors $^i + 2^j + 3^k$ , $2^i -^j +^k$ and $3^i +^j + 4^k$ 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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Coplannar but can 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 Coplannar but can form a triangle
$\begin{matrix} ˆ i + 2 ˆ j + 3 ˆ k 2 ˆ i - ˆ j + ˆ k 3 ˆ i + ˆ j + 4 ˆ k ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 2 & - 1 & 1 3 & 1 & 4 \end{matrix} ∣ ∣ ∣ ∣ = 1 (- 4 - 1) - 2 (8 - 3) + 3 (2 + 3) = - 5 - 10 + 15 = 0 S o, v e c t o r s a r e c o p l a n e r . o p t i o n C i s c o r r e c t a n s w e r . \end{matrix}$

Suggest Corrections

Similar questions

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

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

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

\to c = 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

3^i - 2^j +^k,^i - 3^j + 5^k

2^i +^j - 4^k

2^i -^j +^k,^i - 3^j - 5^k

3^i - 4^j - 4^k

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