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Sum

If `bar"AB" = 2hat"i" - 4hat"j" + 7hat"k"` and initial point A(1, 5, 0). Find the terminal point B.

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#### Solution

Let `bar"a"` and `bar"b"` be the position vectors of A and B.

Given: A(1, 5, 0)

∴ `bar"a" = hat"i" + 5hat"j"`

Now, `bar"AB" = 2hat"i" - 4hat"j" + 7hat"k"`

∴ `bar"b" - bar"a" = 2hat"i" - 4hat"j" + 7hat"k"`

∴ `bar"b" = (2hat"i" - 4hat"j" + 7hat"k") + bar"a"`

`= (2hat"i" - 4hat"j" + 7hat"k") + (hat"i" + 5hat"j")`

`= 3hat"i" + hat"j" + 7hat"k"`

Hence, the terminal point B(3, 1, 7).

Concept: Representation of Vector

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