What if 3 vectors are coplanar?

If three vectors are coplanar then their scalar product is zero, and if these vectors are existing in a 3d- space. The three vectors are also coplanar if the vectors are in 3d and are linearly independent. If more than two vectors are linearly independent; then all the vectors are coplanar.

What will be the vector triple product of three vector?

Vector product of three vectors a ,b and c of the type a ×(b ×c ) is known as vector triple product.

What is the product of triple scalar of three coplanar vectors?

If there are three vectors in a 3d-space and their scalar triple product is zero, then these three vectors are coplanar.

What is the formula of vector triple product?

Vector Triple Product Properties The vector triple product a × (b × c) is a linear combination of those two vectors which are within brackets. The ‘r’ vector r=a×(b×c) is perpendicular to a vector and remains in the b and c plane.

What is scalar triple product?

The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.

What is coplanar line?

Glossary Term: Coplanar Line Definition. A line which is in the same plane as another line. Any two intersecting lines must lie in the same plane, and therefore be coplanar.

What is AXB XC?

(a x b) x c = (a c)b – (b c)a (1) for the repeated vector cross product. This vector-valued identity is easily seen to be. completely equivalent to the scalar-valued identity.

What is the scalar triple product?

The scalar triple product of three vectors a, b, and c is (a×b)⋅c. The scalar triple product is important because its absolute value |(a×b)⋅c| is the volume of the parallelepiped spanned by a, b, and c (i.e., the parallelepiped whose adjacent sides are the vectors a, b, and c).

How do you know if a vector is coplanar?

If the scalar triple product of any three vectors is zero then they are coplanar. If any three vectors are linearly dependent then they are coplanar. n vectors are coplanar if among them no more than two vectors are linearly independent vectors.

What is AXB xC?

Can you multiply three vectors?

Especially useful is the mixed product of three vectors: a·(b×c) = det(a b c), where the dot denotes the scalar product and the determinant det(a b c) has vectors a, b, c as its columns. The determinant equals the volume of the parallelepiped formed by the three vectors.

What is coplanar example?

Points or lines are said to be coplanar if they lie in the same plane. Example 1: The points P , Q , and R lie in the same plane A . They are coplanar .

What is a coplanar triple product?

If the scalar triple product of any three vectors is 0, then they are called coplanar. The vectors are coplanar if any three vectors are linearly dependent, and if among them not more than two vectors are linearly independent. FAQs (Frequently Asked Questions) 1.

What is the scalar triple product of three vectors?

The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two. is the (signed) volume of the parallelepiped defined by the three vectors given.

How do you prove that three vectors are coplanar?

1 If there are three vectors in a 3d-space and their scalar triple product is zero, then these three vectors are coplanar. 2 If there are three vectors in a 3d-space and they are linearly independent, then these three vectors are coplanar. 3 In case of n vectors, if no more than two vectors are linearly independent, then all vectors are coplanar.

How to prove the vector triple product is right?

We need to prove that the vector triple product is the right result generated from the cross product of →a, →b, and→c. This product can be written as the linear combination of vectors →aand→b. Now, we have (→a × →b) × →c = x→a + y→b……