Definition: Set of integers is denoted by Z and defined as: Z = {0, ±1, ±2, ±3,... } Set of positive integers Z+ = {1, 2, 3, ...
If a and b are unit vectors and θ is the angle between them, then how do I prove that sin θ/2 = ½ |a-b|?
Show that a is perpendicular to b iff |a + b| = |a - b|.
Prove that the three points -2a + 3b + 5c, a + 2b + 3c and 7a - c are colinear, where a, b, c are non-coplanar.
Prove that the four points 2a + 3b - c, a - 2b + 3c, 3a + 4b -2c and a - 6b + 6c are coplanar, where a, b, c are no-coplanar Prove t...
Prove that the vectors 3a - 7b - 4c, 3a - 2b + c , a + b + 2c are coplaner, where a, b, c are non-coplaner vectors. Prove that the v...
Prove that four points -6a + 3b + 2c , 3a - 2b + 4c , 5a + 7b + 3c and -13a + 17b - c are coplanar, where a,b,c are non-coplanar. P...
Linearly Independent Vectors Linearly Independent Vector Linearly Dependent Vectors Linearly Dependent Vector Some Importa...
Show that the vectors 5a + 6b + 7c, 7a - 8b + 9c, 3a + 20b + 5c are coplanar. Where a, c, and c are non-coplanar.
Prove that the sum of three vectors determined by the diagonals of the three adjacent faces of a cube passing through the same corner, th...
Prove that four diagonals of a parallelepiped and the straight lines joining the midpoints of opposite edges are concurrent at the point ...
Three edges of unit cube through origin O represent the vectors i, j, k respectively. Write down the expression for the vector represent...
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Show that the vectors 5a + 6b + 7c, 7a - 8b + 9c, 3a + 20b + 5c are coplanar. Where a, c, and c are non-coplanar.
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Prove that the four points 2a + 3b - c, a - 2b + 3c, 3a + 4b -2c and a - 6b + 6c are coplanar, where a, b, c are no-coplanar Prove t...
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If a and b are unit vectors and θ is the angle between them, then how do I prove that sin θ/2 = ½ |a-b|?
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Prove that the three points -2a + 3b + 5c, a + 2b + 3c and 7a - c are colinear, where a, b, c are non-coplanar.
