Question

What are the components of a vector which is the sum of the two vectors, V⃗ 1 and V⃗ 2, whose components are (7.8,−3.5,0.0) and (4.3,−8.0,−4.7)?

Answer 1

\[\vec V_1=({V_1}_x,{V_1}_y,{V_1}_z)\\\vec V_2=({V_2}_x,{V_2}_y,{V_2}_z)\]

\[\vec V_3=\vec V_1+\vec V_2\\
\quad=({V_1}_x,\,{V_1}_y,\,{V_1}_z)\ +\ ({V_2}_x,{V_2}_y,\,{V_2}_z)\\
\quad=({V_1}_x+{V_2}_x,\quad {V_1}_y+{V_2}_y,\quad {V_1}_z+{V_2}_z)\]

Answer 2

The resultant vector, has components equal to the sums of the corresponding components of the composing vectors.

Answer 3

Oh!! Thank you so much for your help :)!

Answer 4

What is the length of this vector? How do I know?

Answer 5

Find the length with pythagorus

\[|V_3|=\sqrt{{V_3}_x^2+ {V_3}_y^2+ {V_3}_z^2}\\\qquad=\sqrt{({V_1}_x+{V_2}_x)^2+ ({V_1}_y+{V_2}_y)^2+ ({V_1}_z+{V_2}_z)^2}\]