Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
If the scalar is > 1 the resultant vector will be larger and in the same direction. = 1 the resultant vector will be the same as the original vector. between 0 and 1 the resultant vector will be smaller and in the same direction. = 0 the resultant vector will be null. If the scalar is less than 0, then the pattern will be the same as above except that the direction of the resultant will be reversed.
by method of finding resultant
Yes, you can add anything to null vector.
Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
If vector equation A + B = 0, it means that vector B is equal in magnitude but opposite in direction to vector A. Therefore, the magnitude of vector B is equal to the magnitude of vector A.
The zero vector, denoted as 0, is a vector with all components equal to zero. It serves as the additive identity element in vector spaces, meaning that adding it to any vector does not change the vector's value.
If the scalar is > 1 the resultant vector will be larger and in the same direction. = 1 the resultant vector will be the same as the original vector. between 0 and 1 the resultant vector will be smaller and in the same direction. = 0 the resultant vector will be null. If the scalar is less than 0, then the pattern will be the same as above except that the direction of the resultant will be reversed.
0 is a cross product of a vector itself
Yes, you can add anything to null vector.
by method of finding resultant
import java.util.Vector; public class VectorTest { /** * @param args */ public static void main(String[] args) { //instantiating a vector Vector vct = new Vector(); //Add objects to a vector vct.add("One"); //getting values from the vector String val = (String) vct.get(0); //vector size System.out.println("Vector size is: " + vct.size()); //removing elements from a vector vct.remove(0); } }
The multiplicative resultant is a three unit vector composed of a vector parallel to the 3 unit vector and a vector parallel to the product of the 3 unit and 4 unit vectors. R = (w4 + v4)(0 +v3) = (w40 - v4.v3) + (w4v3 + 0v4 + v4xv3) R = (0 - 0) + w4v3 + v4xv3 as v4.v3 =0 ( right angles or perpendicular)
Yes, any number can be added to a null vector.
The zero vector has no magnitude. v= Io + Jo + k0 has no magnirude |V|= sqroot(o^2 + 0^2 + 0^2)=0.