Scalar And Vector Quantities - SS1 Physics Past Questions and Answers - page 3

The minimum magnitude of the resultant vector when subtracting two vectors occurs when the vectors are in opposite directions. In this case, the magnitude of the resultant vector is the difference between the magnitudes of the two vectors: * 8 units - 6 units = 2 units.

To add the two vectors, we simply add their corresponding components.

C = (3i + 2j) + (-2i + 4j)

C = (3 - 2)i + (2 + 4)j

C = i + 6j

C = i + 6j

 

To subtract the two vectors, we subtract their corresponding components.

R = (5i - 3j) - (2i + 7j)

R = (5 - 2)i + (-3 - 7)j

R = 3i - 10j

R = 3i - 10j

 

To calculate the vector C, we first multiply vector A by 2 and then subtract vector B.

C = 2(4i - 6j) - (-2i + 8j)

C = 8i - 12j + 2i - 8j

C = 10i - 20j

C = 10i - 20j

 

To calculate the vector R, we add vectors P and Q, and then subtract vector P.

R = (3i - 4j) + (-2i + 6j) - (3i - 4j)

R = 3i - 4j - 2i + 6j - 3i + 4j

R = -2i + 6j

R = -2i + 6j

The resolution of a vector into its components involves breaking down a vector into two or more vectors that, when added together, result in the original vector. This process fundamentally utilizes the Pythagorean theorem (for right-angled components) to determine the magnitudes of the components.