First slide

Scalars and Vectors

Question

Two vectors have magnitudes 6 units and 8 units, respectively. Find magnitude of resultant of two vectors if angle between two vectors is $120 °$

Easy

A

$\sqrt{48}$ units
B

$\sqrt{52}$ units
C

$\sqrt{58}$ units
D

$\sqrt{60}$ units

Solution

Magnitude of vector A=6 Units.
Magnitude of vector B=8 units.
Now resultant $= | A + B |$ will be equal to $\sqrt{A^{2} + B^{2} + 2 A B \cos (θ)}$
when angle between them is 120 degree:
Then $| A + B | = \sqrt{6^{2} + 8^{2} + (2) (6) (8) \cos (120)}$
$= \sqrt{100 - 48} (s i n c e \cos (120) = - 1 / 2)$
$= \sqrt{52}$ units

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