If the scalar triple product of 3 vectors a-b- and c-is 0 - then they are coplanar-

Look, when the volume of the parallelopipped spanned by a⃗,b⃗ and c⃗ is zero, that means it’s a flat parallelopipped with no height. It clearly means that when ...

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Standard XII

Mathematics

Scalar Triple Product

If the scalar...

Question

If the scalar triple product of 3 vectors $\to a, \to b a n d \to c$ is 0 , then they are coplanar.

True

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False

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Solution

The correct option is A
True

Look, when the volume of the parallelopipped spanned by $\to a, \to b a n d \to c$ is zero, that means it’s a flat parallelopipped with no height. It clearly means that when it’s a flat one, then all the vectors are in one plane i.e., they are coplanar.

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Similar questions

If the scalar triple product of 3 vectors $\to a, \to b a n d \to c$ is 0 , then they are coplanar.

Q. If

\to a, \to b

and

\to c

are unit coplanar vectors then the scalar triple product

[2 \to a - \to b 2 \to b - \to c 2 \to c - \to a]

is equal to

Q. Assertion :Vectors

\to a = - λ^{2}^i +^j +^k, \to b =^i - λ^{2}^j +^k

and

\to c =^i +^j - λ^{2}^k

are coplanar for only two values of

λ

. Reason: If vector

¯ x, ¯ y, ¯ z

are coplanar, then scalar triple product is zero.

Q. If

\to a, \to b, \to c

are three unit vectors, each is inclined at an angle

\frac{π}{3}

with the other, then scalar triple product

[\to a \to b \to c]

equals

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If the scalar triple product of 3 vectors →a,→b and →cis 0 , then they are coplanar.

The correct option is A True Look, when the volume of the parallelopipped spanned by →a,→b and →c is zero, that means it’s a flat parallelopipped with no height. It clearly means that when it’s a flat one, then all the vectors are in one plane i.e., they are coplanar.

If the scalar triple product of 3 vectors $\to a, \to b a n d \to c$ is 0 , then they are coplanar.

The correct option is A
True

Look, when the volume of the parallelopipped spanned by $\to a, \to b a n d \to c$ is zero, that means it’s a flat parallelopipped with no height. It clearly means that when it’s a flat one, then all the vectors are in one plane i.e., they are coplanar.