Final answer:
The statement is False because the equation for a plane passing through the origin with the given normal vector should be 2x+2y+3z=0, without the constant term.
Step-by-step explanation:
The statement 'The equation of the plane that passes through the origin with the normal vector ⟨2,2,3⟩ is : 2x+2y+3z−1=0' is False. To find the equation of a plane that passes through the origin and has a normal vector n=⟨a,b,c⟩, you use the equation ax+by+cz=0. In this case, with the normal vector ⟨2,2,3⟩, the equation would be 2x+2y+3z=0. The constant term in the provided equation (-1) indicates that the plane does not pass through the origin.
Some concepts related to vectors and planes from physics are that a vector can indeed form the shape of a right angle triangle with its x and y components, and the Pythagorean theorem can be used to calculate the length of the resultant vector when two vectors are at right angles to each other. Moreover, vector components can be expressed as the projection onto their respective axes.