If the sum of two unit vectors is a unit vector, then magnitude of difference is - (a) √2 (b) √3 (c) 2√2 (d) √5

By Ritesh|Updated : November 9th, 2022

If the sum of two unit vectors is a unit vector, then the magnitude of the difference is √3. Steps to find the magnitude of the difference:

Consider two unit vectors a, and b, whose sum is also a unit vector, c.

a + b = c and |a| = |b| = |c| = 1

Now, we know that magnitude of the sum of a and b is:

|a + b|2 = |a|2 + |b|2 + 2 (ab cosθ)

Substituting the values we get:

1 = 1 + 1 + 2 (ab cosθ)

ab cosθ = -½

Magnitude of their difference is given by:

|a - b|2 = |a|2 + |b|2 - 2 (ab cosθ)

Substituting the values we get:

1 + 1 - 2 x -½ = 3

|a - b| = √3

Magnitude of a Vector

The definition of a vector is an entity with both magnitude and direction. The movement of an object between two points is described by a vector. The directed line segment can be used to graphically represent vector math.

The magnitude of a vector is the length of the directed line segment, and the vector's direction is indicated by the angle at which it is inclined. A vector has a "Tail" at its beginning and a "Head" at its finish, both of which include arrows.

A mathematical structure is referred to as a vector. It has a wide range of uses in physics and geometry. We understand that the coordinates of the points on the coordinate plane can be expressed using an ordered pair, such as (x, y). The vector method is highly helpful in the three-dimensional geometry reduction procedure.

Summary:

If the sum of two unit vectors is a unit vector, then the magnitude of difference is -(a) √2(b) √3(c) 2√2(d) √5

If the sum of two unit vectors is a unit vector, then the magnitude of difference is √3. A vector is defined as a thing that has both magnitude and direction. A vector describes how an object moves between two places.

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