VECTOR ANALYSIS
Q-Define vectors and scalars. Give two examples of each.
A- Vectors are quantities that have both magnitude and direction. Examples are displacement, weight, acceleration, etc. Scalars are quantities that have only magnitude and no direction. Examples are speed, time, frequency, etc.
Q- Define the following terms.
Negative vector,equal vector,collinear vector,coplanar vector,zero vector
A-(i) Negative of a vector: It has the same magnitude but opposite direction of the given vector.
(ii) Equal vectors: If two vectors have equal magnitude and direction, they are equal vectors.
(iii) Collinear vectors: Two vectors acting along the same straight lines or along parallel straight lines in the same direction or in the opposite direction are called collinear vectors.
(iv) Coplanar vectors: If three or more vectors lie in the same plane, then they are called coplanar vectors.
(v) Zero vector: It is a vector with zero magnitude and no specific direction.
Q-Define law of triangle for vector addition.
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A- If two sides of a triangle are shown by two continuous vectors (vector A and vector B), then the third side of the triangle in the opposite direction shows the resultant of two vectors (vector C).
C=A+B
Q-state and prove –Parallelogram Law of Vectors
A-If two vectors act along two adjacent sides of a parallelogram having a magnitude equal to the length of the sides, both pointing away from the common vertex, then the resultant is given by the diagonal of the parallelogram passing through the same common vertex and in the same sense as the two vectors.
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Q-Explain dot product or scalar project of two vectors. Give two examples also.
A- watch video solutions.click below.
Q-If addition and subtraction of vectors are equal then find the angle between these two vectors.
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Q-Resultant of two vectors P & Q is R. If direction of Q is reversed then resultant is S . prove that
2 (P^2+ Q^2) = R^2 +S^2
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