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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

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### Vector Addition in Component form

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What is the component form of a vector?

• components along x, y, and z axes
• components along x, y, and z axes
• magnitude of the vector
• directional cosines of vector

Answer is 'components along x, y, and z axes'

In the component form, two vectors are considered a i and p i. What is the result of addition of two vectors a i and p i ?

• (a+p)i
• (a+p)i

Answer is '(a+p)i'.
The magnitudes add up as two vectors are in the same direction i , that is, along x-axis.

What is the result of addition of two vectors ai+bj and p i ?

• (a+p)i+bj
• (a+p)i+bj
• cannot be added, as the vectors are in different directions.

Answer is '(a+p)i+bj'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In this problem, in the direction of x-axis, a i and p i are given. They are added in magnitude.

What is the result of addition of two vectors a i+b j+c j and p i+q j+r k ?

• (a+p)i+(b+q)j+(c+r)k
• (a+p)i+(b+q)j+(c+r)k
• cannot be added, as the vectors are in different directions.

Answer is '(a+p)i+(b+q)j+(c+r)k'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In these two vectors, the components along the three axes are given in component form.

When vectors in the component form are added, the corresponding components are added.

Addition of two vectors: When two vectors vec p = p_x i+p_yj+p_zk and vec q = q_x i+q_yj+q_zk are added the result is vec p + vec q = (p_x+q_x)i + (p_y+q_y)j + (p_z+ q_z)k

slide-show version coming soon