Question Video: Find the Displacement Vector | Nagwa Question Video: Find the Displacement Vector | Nagwa

# Question Video: Find the Displacement Vector Mathematics • Third Year of Secondary School

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Given π = <6, 1, 4> and π = <3, 1, 2>, find ππ.

02:20

### Video Transcript

Given vector π equals six, one, four and vector π equals three, one, two, find ππ.

We recall that to find ππ, we subtract vector π from vector π. The reason for this can be shown on a two-dimensional grid. This can then be transferred to three-dimensional vectors.

Letβs consider two points on the grid, A and B. The vector π is given from its displacement from the origin O. The same is true of vector π. We wish to travel from point A to point B. This is the same as traveling from point A to point O and then point O to point B. Going from point A to point O would be equivalent to negative vector π. And going from point O to point B is equivalent to vector π. ππ is equal to negative vector π plus vector π. This can be rewritten as vector π minus vector π.

Weβre told in this question that vector π is equal to six, one, four. This could also be written as a column vector as shown. It is also sometimes written in terms of vectors π’, π£, and π€. In this case, six π’ plus π£ plus four π€, where six, one, and four are the coefficients of π’, π£, and π€.

For the purposes of this question, we will stick with the notation given. And weβre also told that vector π is equal to three, one, two. In order to calculate π minus π, we simply subtract the individual components. Three minus six is equal to negative three. One minus one is equal to zero. Finally, two minus four is equal to negative two. ππ is therefore equal to negative three, zero, negative two.

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