Q: If the sum of the two unit vectors is also a unit vector find the magnitude of their difference?

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I think so, yes; that's basically what the concept of a "vector" in physics is all about. (There are also more abstract vectors in math and physics, but something that has a magnitude and a direction would be enough to quality as a vector.)

Vectors are used whenever there is a measurement in which not only the magnitude is relevant, but also the direction. Typical uses of vectors include position, velocity, acceleration, force, torque, and others.

Yes. Any number of vectors, two or more, can result in zero, if their magnitudes and directions are just right. One vector can result in zero only if its magnitude is zero.

We can't answer that without also knowing the magnitude of the individual vectors.

No. For three vectors they must all lie in the same plane. Consider 2 vectors first. For them to resolve to zero, they must be in opposite direction and equal magnitude. So they will lie along the same line. For 3 vectors: take two of them. Any two vectors will lie in the same plane, and their resultant vector will also lie in that plane. Find the resultant of the first two vectors, and the third vector must be along the same line (equal magnitude, opposite direction), in order to result to zero. Since the third vector is along the same line as the resultant vector of the first two, then it must be in the same plane as the resultant of the first two. Therefore it lies in the same plane as the first two.

Related questions

Yes, the resultant is a vector quantity because it has both magnitude and direction. It is the vector sum of two or more vectors acting on a system.

Vectors can be added using the component method, where you add the corresponding components of the vectors to get the resultant vector. You can also add vectors using the graphical method, where you draw the vectors as arrows and then add them tip-to-tail to find the resultant vector. Additionally, vectors can be added using the trigonometric method, where you use trigonometry to find the magnitude and direction of the resultant vector.

I think so, yes; that's basically what the concept of a "vector" in physics is all about. (There are also more abstract vectors in math and physics, but something that has a magnitude and a direction would be enough to quality as a vector.)

No, not necessarily. A vector is a quantity that has both magnitude and direction. While it can have positive and negative values, not all quantities with positive and negative values represent vectors. Vectors must also obey the rules of vector addition and scalar multiplication.

Vectors are used whenever there is a measurement in which not only the magnitude is relevant, but also the direction. Typical uses of vectors include position, velocity, acceleration, force, torque, and others.

A vector consists of a magnitude (length) and a direction in space. It is typically represented by an arrow showing magnitude and direction, and may also have components along different axes. Vectors are used in physics and mathematics to represent quantities like force, velocity, and displacement.

Scalar and vector quantities are both used in physics to describe properties of objects. They both have magnitude, which represents the size or amount of the quantity. However, the key difference is that vector quantities also have direction associated with them, while scalar quantities do not.

Construct the rectangle that contains the right angle subtended by the vectors. Calculate or construct the diagonal of the rectangle. The diagonal is the hypotenuse of a right triangle with the two vectors as sides. The hypotenuse is also the vector that is the sum of the two original vectors. Calculate the magnitude of that vector by applying the theorem.

Vectors can be represented graphically using arrows. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction in which the vector is pointing. Vectors can also be represented by coordinates in a coordinate system.

Yes. Any number of vectors, two or more, can result in zero, if their magnitudes and directions are just right. One vector can result in zero only if its magnitude is zero.

Scalar quantities are represented by a magnitude only, such as time or temperature, while vector quantities have both magnitude and direction, like displacement or velocity. Scalars can be added or subtracted algebraically, whereas vectors require vector addition that considers both magnitude and direction. Scalars are also simpler to work with mathematically, while vectors require more complex operations.

We can't answer that without also knowing the magnitude of the individual vectors.