WASSCE SHS
A vector has magnitude and direction. In component form you add the matching components. The magnitude is the square root of the sum of the squares of the components.
Write a vector as a column, or as ai + bj. To add, add the i components and add the j components. To multiply by a scalar, multiply each component by that scalar. Subtraction is adding the negative. The zero vector has both components zero. These operations do not change the rules of ordinary arithmetic inside each component. A sign error in one component leaves the other component able to score.
The magnitude of ai + bj is the square root of a² + b². It is a length, so it is not negative. You do not need to simplify a square root unless the question says so, but √13 is better left as √13 than as a rounded decimal the question did not request. A unit vector in the same direction is the vector divided by its magnitude. Direction can also be given as an angle with the horizontal, using tangent. This page asks for a sum and a magnitude.
Components stay in their places. Adding the i component of one vector to the j component of the other is a method error. Magnitude uses Pythagoras on the components of the vector you were asked about, not on the sum, unless the question asked for the magnitude of the sum. Leave the answer in surd form when it is exact.
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
4 marks
a = 3i + 2j and b = i − 4j.
(a) Find a + b. (2 marks)
(b) Find the magnitude of a. (2 marks)
(a) a + b = 4i − 2j.
(b) |a| = square root of (3² + 2²) = square root of 13.
2 marks
Find 2a − b. (2 marks)
2a = 6i + 4j. 2a − b = 6i + 4j − i + 4j = 5i + 8j.
1 mark
Explain why the magnitude of a vector cannot be negative. (1 mark)
Magnitude is a length. A length is zero or positive.
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Elective Mathematics freeAdd the i components and add the j components. If a is 3i + 2j and b is i − 4j, then a + b is 4i − 2j. Do not add an i component to a j component.
Square each component, add the squares, and take the square root. The magnitude of 3i + 2j is the square root of 13. It is positive. All WASSCE Elective Mathematics past questions