Given two vectors a = 3.4i -3.4j and b =6.4i+8.8j,find the magnitude (in m) of the vector a.
Find the direction (in ° = deg) of the vector a.
Find the magnitude of the vector b.
Find the direction (in °) of the vector b.
Find the magnitude of the vector a+b.
Its direction?
Find the magnitude of the vector b-a.
Its direction?
Find the magnitude of the vector a-b.
Its direction?
Find magnitude????
a = 3.4i - 3.4j
b = 6.4i + 8.8j
1) |a| = √( (3.4)² + (-3.4)² ) ≈ 4.8083
2) Ɵa = arctan(-3.4/3.4) ≈ -45°
3) |b| = √( (6.4)² + (8.8)² ) ≈ 10.8811
4) Ɵb = arctan(8.8/6.4) ≈ 53.97°
5) |a+b| = √( (3.4+6.4)² + (-3.4+8.8)² ) ≈ 11.1892
6) Ɵ(a+b) = arctan(5.4/9.8) ≈ 28.8556°
7) |b-a| = √( (6.4-3.4)² + (8.8-(-3.4))² ) ≈ 12.5634
8) Ɵ(b-a) = arctan(12.2/3) ≈ 76.1849°
9) |a-b| = √( (3.4-6.4)² + (-3.4-8.8)² ) ≈ 12.5634
10) Ɵ(a-b) = arctan(-12.2/-3) ≈ 76.1849°
Reply:Hi,
Given two vectors a = 3.4i -3.4j and b =6.4i+8.8j,find the magnitude (in m) of the vector a.
|a| = √(3.4² + 3.4²) = 4.81 %26lt;== ANSWER
Find the direction (in ° = deg) of the vector a.
tan^(-1) (3.4/-3.4) = tan^(-1) (-1) = -45° ( or 315°) %26lt;== ANSWER
Find the magnitude of the vector b.
|b| = √(6.4² + 8.8²) = 10.88 %26lt;== ANSWER
Find the direction (in °) of the vector b.
tan^(-1) (6.4/8.8) = tan^(-1) (-1) = 36.03° %26lt;== ANSWER
Find the magnitude of the vector a+b.
a+b = 9.8i + 5.4j
|a + b| = √(9.8² + 5.4²) = 11.19 %26lt;== ANSWER
Its direction?
tan^(-1) (5.4/9.8) = 28.86° %26lt;== ANSWER
Find the magnitude of the vector b-a.
b - a = 6.4i+8.8j - (3.4i -3.4j) = 3i + 12.2j
|b - a| = √(3² + 12.2²) = 12.56 %26lt;== ANSWER
Its direction?
tan^(-1) (12.2/3) = 76.18° %26lt;== ANSWER
Find the magnitude of the vector a-b.
(3.4i -3.4j) - (6.4i+8.8j) = -3i - 12.2j
|a - b| = √((-3)² + 12.2²) = 12.56 %26lt;== ANSWER
Its direction?
tan^(-1) (-12.2/-3.1) = 255.74° %26lt;== ANSWER
I hope that helps!! :-)
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