The vectors having the same initial point are called
Co-Initial vector
Co-Initial Vectors: Definition and Explanation
Vectors that share the same starting point are specifically referred to as Co-Initial vectors.
What are Co-Initial Vectors?
In the study of vectors, Co-Initial vectors are defined as a set of two or more vectors that originate from the exact same initial point in space. While these vectors can differ in their magnitude (length) and direction, the crucial aspect that defines them as co-initial is their common starting position.
Understanding Other Vector Types
To fully grasp why "Co-Initial vector" is the correct terminology, let's briefly examine the other provided options:
- Position Vector: This type of vector is used to describe the location of a point in space relative to a fixed reference point, typically the origin (0,0). Its initial point is always the origin.
- Free Vector: A free vector is one whose initial point is not fixed. It can be moved anywhere in space (translated) without altering its magnitude or direction.
- Unit Vector: A unit vector is characterized by having a magnitude equal to 1. Unit vectors are primarily used to indicate direction.
Key Distinction
The defining feature of Co-Initial vectors is simply that they have the same initial point, differentiating them from vectors that may start at different points or have origins defined by their position or lack thereof.
Important Questions from Properties of Vectors
If \(\rm \left [\vec a \times \vec b,\ \vec b \times \vec c,\ \vec c \times \vec a \right]\) = 64 then \(\rm \left [\vec a\ \vec b\ \vec c \right]\)is
In a triangle ABC, if taken in order, consider the following statements;
1) \(\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = \vec 0\)
2) \(\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} = \vec 0\)
3) \(\overrightarrow {AB} - \overrightarrow {BC} + \overrightarrow {CA} = \vec 0\)
4) \(\overrightarrow {BA} - \overrightarrow {BC} + \overrightarrow {CA} = \vec 0\)
How many of the above statements are correct?
Let \({\rm{\vec p}}\) and \({\rm{\vec q}}\) be the position vectors of the points P and Q respectively with respect to origin O. The points r and S divide PQ internally and externally respectively in the ratio 2 : 3 If \(\overrightarrow {{\rm{OR}}}\) and \(\overrightarrow {{\rm{OS}}}\) are perpendicular, then which one of the following is correct?
What is \(\left( {\vec a - \vec b} \right) \times \left( {\vec a + \vec b} \right)\) equal to?
If the vectors \(a\hat i + \hat j + \hat k,\;\hat i + b\hat j + \hat k\) and \(\hat i + \hat j + c\hat k\;\left( {a,\;b,\;c \ne 1} \right)\) are coplanar, then the value of \(\frac{1}{{1 - a}} + \frac{1}{{1 - b}} + \frac{1}{{1 - c}}\) is equal to
