Two forces of magnitudes 8N and 15N act at a point. If the resultant force is 17N, the angle between the forces has to be:
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Use R² = F₁² + F₂² + 2F₁F₂cosθ.
Two forces of magnitude 7N and 5N act on a particle at an angle θ to each other. θ can have any value. The minimum magnitude of the resultant force is:
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The minimum resultant occurs when the forces are anti-parallel.
If two forces F and G act at right angles to each other, their resultant has the magnitude:
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For perpendicular vectors, use the Pythagorean relation.
Two forces of the same magnitude act at a point. The square of their resultant is 3 times the product of their magnitudes. The angle between them is:
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Use R² = F² + F² + 2F²cosθ.
Two forces of magnitudes F₁ and F₂ acting at right angle to each other have the resultant of magnitude:
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Perpendicular vectors combine by the Pythagorean theorem.
Two forces each of 10N magnitude act on a body. If the forces are inclined at 30° and 60° with x-axis, then the x-component of their resultant is:
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Add the x-components: 10cos30° + 10cos60°.
Angle between the vectors (i + j) and (j + k) is:
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Use the dot product and magnitudes of the two vectors.
The resultant of two forces 3N and 4N making an angle 90° with each other is:
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The x-component of a force vector F of magnitude 30N making an angle of 60° with x-axis is:
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Two forces (P+Q) and (P−Q), acting at a point have their resultant √[2(P²+Q²)]. Then the angle between them must be:
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Compare the resultant formula with the given magnitude.
Torque is also known as:
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Torque is the moment of a force.
If |a + b| = |a − b|, then the angle between a and b is:
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Squaring both sides gives a·b = 0.
If |F₁ × F₂| = |F₁ · F₂|, then |F₁ + F₂| is:
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The equality gives θ = 45°; then use the vector-addition magnitude formula.
One of two forces is double the other and their resultant is equal to the greater force. The angle between them is:
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Let the forces be F and 2F and apply the law of cosines for the resultant.
To get a resultant displacement of 10 cm, two displacement vectors one of magnitude 6 cm and another of 8 cm should be combined:
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If A = B + C and the magnitudes of A, B and C are 5, 4 and 3 units, respectively, the angle between A and C is:
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Use A·C = (B+C)·C and the given magnitudes.
Torque acting on a body determines its:
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Torque is the rotational analogue of force and produces angular acceleration.
The rotational analogue of forces is:
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Torque plays the rotational role corresponding to force.
If both Rₓ and Rᵧ are negative, the resultant lies in the:
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Negative x and negative y components place a vector in quadrant III.
