Find the resultant of the following vectors:

a) i + j - k and i + 2j - k [2 Marks]

b) 2i - j + 3k and i - j - k [2 Marks]

To find the resultant of vectors, you simply add the corresponding components of each vector together. Let's solve each part step-by-step.
Part a:
You have two vectors: A = i + j − k and B = i + 2 j − k .
To find the resultant vector R , you add the corresponding components from each vector:

The i -components: 1 + 1 = 2 i
The j -components: 1 + 2 = 3 j
The k -components: − 1 − 1 = − 2 k

Thus, the resultant vector R is:
R = 2 i + 3 j − 2 k
Part b:
You have two vectors: C = 2 i − j + 3 k and D = i − j − k .
To find the resultant vector S , add the corresponding components:

The i -components: 2 + 1 = 3 i
The j -components: − 1 − 1 = − 2 j
The k -components: 3 − 1 = 2 k

Thus, the resultant vector S is:
S = 3 i − 2 j + 2 k
In summary:

Resultant of (a): 2 i + 3 j − 2 k
Resultant of (b): 3 i − 2 j + 2 k

These resultant vectors give you the combined effect of their respective vector pairs.

Answered by RyanHarmon181 | 2025-07-06