The branch of surveying in which both horizontal and vertical positions of a point, are determined by making instrumental observations, is known as

the branch of surveying in which both horizontal & Vertical Positions of a points are determined by making istrument observation is known as tacheometry.

tacheometry is the answer for sure

Tacheometry (/ˌtækiˈɒmɨtri/; from Greek for "quick measure"), is a system of rapid surveying, by which the positions, both horizontal and vertical, of points on the earth surface relatively to one another are determined without using a chain or tape or a separate levelling instrument.

I guess option -1- Tacheometry 

The correct answer is:

1: tacheometry

Tacheometry for positioning of both horizontal and vertically.

1: tacheometry is the correct answer.

First Answer tacheometry                                 .

1: tacheometry

2: tachemetry

3: telemetry

""4: all the above""

Thank you miss Elke Woofter or the beautiful explained answer