a) The sum of vector v1 and vector v2 is 5i+5j
b) The difference between vector v1 and vector v2 is 1i + 3j
c) The difference between v2 and v1 is -1i-3j
d) The sum of the vector 3v1 and vector is 13i + 14j
e) The sum of vector -4v1 and vector 2v2 is -8i+18j
f) The difference between vector 0.5v1 and vector 0.6v2 is 0.3i + 1.4j
Vectors are quantities that have both magnitude and direction. Vectors can be added together, subtracted from ach other and multiplied together.
Given the vector
v1 = 3m/s ˆi + 4m/s ˆj
v2 = 2m/sˆi +1m/sˆj,
a) Taking the sum of the vectors.
v1 + v2 = (3 ˆi + 4 ˆj ) + (2 ˆi + 1 ˆj)
Collecting the like that
v1 + v2 = (3i+2i)+(4j+1j)
v1 + v2 = 5i + 5j
b) Taking the difference of the vectors.
v1 + v2 = (3 ˆi + 4 ˆj ) - (2 ˆi + 1 ˆj)
Collecting the like that
v1 - v2 = (3i-2i)+(4j-1j)
v1 - v2 = 1i + 3j
c) Taking the difference of the vectors.
v2 - v1 = (2 ˆi + 1 ˆj ) - (3 ˆi + 4 ˆj)
Collecting the like that
v1 - v2 = (2i-3i)+(1j-4j)
v1 - v2 = -1i + (-3j)
v1 - v2 = -1i - 3j
d) 3 ∗ v1 + 2 ∗ v2
= 3(3i+4j) + 2(2i+j)
= 9i + 12j + 4i + 2j
= 9i + 4i + 12j + 2j
= 13i + 14j
e) -4 ∗ v1 + 2 ∗ v2
= -4(3i+4j) + 2(2i+j)
= -12i + 16j + 4i + 2j
= -12i + 4i + 16j + 2j
= -8i + 18j
f) 0.5 ∗ v1 − 0.6 ∗ v2
= 0.5(3i + 4j) - 0.6(2i + j)
= 1.5i + 2.0j - 1.2i - 0.6j
Collect the like terms
= 1.5i - 1.2i + 2.0j - 0.6j
= 0.3i + 1.4j
Learn more about vectors here: brainly.com/question/14057263
