What is the value of two perpendicular vectors?

What is the value of two perpendicular vectors?

We begin by recalling that two vectors are perpendicular if their dot or scalar product is equal to zero. This means that we begin this question by finding the dot product of vector 𝐀 and vector 𝐁, where vector 𝐀 is equal to two, two, negative six and vector 𝐁 is equal to three, three, 𝑘.

What happens when two vectors are mutually perpendicular?

Originally Answered: When unit vectors are mutually perpendicular to each other, what happens during dot product and vector product and why? The dot product will be 0 as they are perpendicular to each other. The cross product will be another vector which will be perpendicular to both unit vectors.

What is mutually perpendicular vectors?

Two vectors and whose dot product is. (i.e., the vectors are perpendicular) are said to be orthogonal. In three-space, three vectors can be mutually perpendicular. SEE ALSO: Dot Product, Orthogonal Basis, Orthonormal Basis, Orthonormal Vectors, Perpendicular.

Is ABC are mutually perpendicular vectors?

If vector a,b,c are mutually perpendicular vectors of equal magnitudes, show that the vector a+b+c is equally inclined to a,b and c. If vector a,b,c are mutually perpendicular vectors of equal magnitudes, show that the vector a+b+c is equally inclined to vector a,b and c.

How do you show that three vectors are perpendicular?

Set the dot-product equal to zero. This is the equation for a plane in three dimensions. Any vector in that plane is perpendicular to U. Any set of three numbers that satisfies 10 v1 + 4 v2 – v3 = 0 will do.

What is the resultant vector if B+C is mutually perpendicular to a?

Since A B Care mutually perpendicular , B+C gives a resultant vector in same plane which is also perpendicular to A . So it gives resultant 0. This is similar to as considering a,b,c as x,y,z vectors… 0. As C is perp. to both A and B so we can say that it is perp. to their place as z axis is perp. to xy plane.

Which vector has to be perpendicular to the x-y plane?

since A,B and C are mutually perpendicular it is necessary for one of them to be perpendicular to the plane in which the other two exists and are perpendicular to each other let B,C are perpendicular vectors in x-y plane then A vector has to be perpendicular to the x-y plane.

What is the dot product of two mutually perpendicular vectors?

Because Dot product of a vector involves cosine of angle between them which is zero (0) for mutually perpendicular vectors as Hence, we conclude, Dot product of two mutually perpendicular vectors is a Null vector . It will be zero as the resultant of B+C would be in same plane as of B and C and dot product with A will be zero The answer is 0.

What is the resultant of addition of two vectors in plane?

Resultant of addition of two vectors in a plane lies in the same plane as the two vectors. Now according to your question A, B, C are mutually perpendicular. Now if B and C to lie in the same plane and are mutually perpendicular their resultant (R) also lies in that plane. As A is perpendicular to plane containing B-C, A.R=0.