Given that the vector ai+ 3j is parallel to the vector 2i + 12j find a? 3i + b is parallel to 12i- 20j find b?

Question

Please explin the calculations step by step
Thank you.

Answer 1

Since ai and 3j are parallel, they have the same slope, and thus their horizontal and vertical components will be proportional. The most direct approach is to set these up as ratios:

a/2 = 3/12.

Cross-multiplying yields ...

12a = 6

a = 0.5

Follow the same procedure for the second group of vectors:

3/12 = b/20

12b = 60

b = 5.
I hope this was helpful.

Answer 2

Question 1
2i + 12 j has gradient 12/2 = 6
Thus 3/a = 6
a = 1/2

Question 2
Assume vector is 3i + bj
12i - 20j has gradient - 20/12 = - 5 / 3
Thus b / 3 = - 5 / 3
b = - 5

Answer 3

ai + 3j = k(2i + 12j) solving a = 2k and 3 = 12k we get a = 0.5
3i + bj = k(12i - 20j) solving 3 = 12k and b = -20k we get b = -5.
remember if two vectors a and b are parallel then a = k times b.

Answer 4

a = 2i b = i + 3j hence a + theta b = 2i + theta(i + 3j) (2+theta)i + 3thetaj if it relatively is parallel to the vector i, the j component must be 0 so 3theta = 0 meaning that theta = 0

Answer 5

a=0.5i
b=5j