Cross Product of Collinear Vectors
In this page, you will learn about the vector cross product between two collinear vectors.
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When two vectors are called 'collinear' vectors?
`color(coral)(text(co)) + color(deepskyblue)(text(linear))` means `color(coral)(text(together))+color(deepskyblue)(text(on a line))`
- the angle between vectors `0^@`
- the angle between vectors `180^@`
- the vectors are parallel
- all the above
- all the above
The answer is 'All the above'
Given the definition of cross product as
`vec p xx vec q = |vec p||vec q|sin theta hat n` What is `vec p xx vec q`, if the given vectors are collinear?
- `|p||q|sin 0 hat n`
- `|p||q|sin 180 hat n`
- `0`
- `0`
- all the above
The answer is 'all the above'. The angle between Collinear vectors can be either `0^@` or `180^@`. And `sin0 = sin180 = 0`.
Given two non-zero vectors `vec p, vec q in bbb V` have `vec p xx vec q = 0`, then what is the angle between the vectors?
- `0^@`
- `0^@`
- `90^@`
- `270^@`
- Any one of the above
The answer is '`0^@`'. It can either be `0^@` or `180^@`.
• Cross product of parallel vectors is 0 or null vector.
Cross Product of Collinear Vectors: For any pair of collinear vectors `vec p, vec q in bbb V`,
`vec p xx vec q =0 `
Angle between vectors when cross product is `0`: For any pair of non-zero vectors `vec p, vec q in bbb V`, If `vec p xx vec q = 0` then the vectors are collinear. The angle between them is `0^@` or `180^@`.
Solved Exercise Problem:
Given `vec p= 2i+3.1j+.5k` and `vec q = 2i+3.1j+.5k` what is the angle between them?
- `90^@`
- `45^@`
- `180^@`
- `0^@`
- `0^@`
The answer is '`0^@`'. The vectors are identical.
Solved Exercise Problem:
Given a vector `vec p` with magnitude `12`, what is `vec p xx vec p`?
- `12`
- `sqrt(12)`
- `12xx12`
- `0`
- `0`
The answer is '`0`'.