te :
1.
Answer all Questions each carries 8 marks.
2. Answer should be comprehensive and the criteria for valuation is
the content but not the length of the answer.
6. (a) Derive an expression for magnitude and direction of resultant of
two Vectors using parallelogram law of vectors.
(or)
(b) Write any four properties of dot product and any four properties of
Cross product.
7. (a) Show that path of a projectile is a parabola in case of oblique
Projection.
(or)
(b) Derive the expression for range and time of flight of a projectile.
Answers
Explanation:
DOT Products:
(1) It is a product of the COMPONENT of one vector along the direction of the other vector.
(2) The product is a SCALAR and therefore has no DIRECTION.
(3) In the DOT PRODUCT of vectors A . B the scalar measure of the product is the product of the magnitudes A & B and the COSINE of the angle between them
Example: work done by a force of 50 N along a displacement of 6 meters at an angle 60 degrees:
Cross Products:
(1) It is the product of TWO VECTORS with the RESULTANT being a VECTOR.
(2) The resultant vector is PERPENDICULAR to the PLANE formed by the two vectors.
(3) The MAGNITUDE of the product is A . B . sine theta. Drawing the vectors in 3-D allows one to notice that the magnitude of the resultant is the AREA of the triangle formed by A * B.
Example: v = 30 m/s East. B = 0.5 T North. q = + e. Then the CROSS PRODUCT: e v X B = (e) (30) (0.5) sin 90 = 15 e N = F and direction of F is in the + z direction.
mark as brainliest thanks