Consider two displacements , one of magnitude 6 meters and another of magnitude 7 meters . Show how the displacement vectors may be combined to get a resultant displacement of magnitude

(a) 13 meters

(b) 1 meter

(c) 8 meters

Explain

[These questions are not clubbed together for convenience . So pls answer them ]

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Solution

a) Angle between them is 0°
7+6=13
They are alligned in the same direction

b) Angle between them is 180°
7-6=1
Alligned in opposite direction

c) r²=a²+b²+2ab cos x
8²=6²+7²+2.6.7cos x
64=36+49+82cos x
64-85=82 cos x
cos x =82/21
Angle x =104.8°

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a) Angle between them is 0° 7+6=13 They are alligned in the same direction b) Angle between them is 180° 7-6=1 Alligned in opposite direction c) r²=a²+b²+2ab cos x 8²=6²+7²+2.6.7cos x 64=36+49+82cos x 64-85=82 cos x cos x =82/21 Angle x =104.8°

a) Angle between them is 0°
7+6=13
They are alligned in the same direction

b) Angle between them is 180°
7-6=1
Alligned in opposite direction

c) r²=a²+b²+2ab cos x
8²=6²+7²+2.6.7cos x
64=36+49+82cos x
64-85=82 cos x
cos x =82/21
Angle x =104.8°