- Vector Algebra
- Show that the straight line joining the mid
points of two sides of a triangle is parallel to third side and is half as
long.
- Prove that diagonal of parallelogram bisect each
other. Conversely if diagonal of a quadrilateral
bisect each other then it is parallelogram.
- Show that medians of a triangle are concurrent.
- Prove that the straight lines joining the mid-points
of the opposite sides of a quadrilateral bisect each other.
- Prove that the diagonal of a parallelogram is
trisected by the straight lines joining with the midpoints of the opposite
sides.
- Three edges of unit cube through origin O represent
the vectors i, j, k respectively. Write down the
expression for the vector represented by
- Prove that four diagonals of a parallelepiped and
the straight lines joining the midpoints of opposite edges are concurrent
at the point of bisection.
- Prove that the sum of three vectors determined by
the diagonals of the three adjacent faces of a cube passing through the
same corner, the vectors being directed from the corner, is twice the
vector determined by the diagonal of the cube passing through the same
corner.
- Show that the vectors 5a + 6b + 7c, 7a - 8b + 9c,
3a + 20b + 5c are coplaner. Where a, c, and c are non-coplaner.
- Linearly Independent and dependent Vectors and
some important points
- Prove that four points -6a + 3b + 2c , 3a - 2b +
4c , 5a + 7b + 3c and -13a + 17b - c are coplaner, where a,b,c are
non-coplanar.
- 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 four points 2a + 3b - c, a - 2b +
3c, 3a + 4b -2c and a - 6b + 6c arw coplanar, where a, b, c are
no-coplaner
- Prove that the three points -2a + 3b + 5c, a + 2b
+ 3c and 7a - c are colinear, where a, b, c are non-coplanar
- Show that a is perpendicular to b iff |a + b| =
|a - b|.
- 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|?
- Vector Algebra
- Show that the straight line joining the mid points of two sides of a triangle is parallel to third side and is half as long.
- Prove that diagonal of parallelogram bisect each other. Conversely if diagonal of a quadrilateral bisect each other then it is parallelogram.
- Show that medians of a triangle are concurrent.
- Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
- Prove that the diagonal of a parallelogram is trisected by the straight lines joining with the midpoints of the opposite sides.
- Three edges of unit cube through origin O represent the vectors i, j, k respectively. Write down the expression for the vector represented by
- Prove that four diagonals of a parallelepiped and the straight lines joining the midpoints of opposite edges are concurrent at the point of bisection.
- Prove that the sum of three vectors determined by the diagonals of the three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube passing through the same corner.
- Show that the vectors 5a + 6b + 7c, 7a - 8b + 9c, 3a + 20b + 5c are coplaner. Where a, c, and c are non-coplaner.
- Linearly Independent and dependent Vectors and some important points
- Prove that four points -6a + 3b + 2c , 3a - 2b + 4c , 5a + 7b + 3c and -13a + 17b - c are coplaner, where a,b,c are non-coplanar.
- 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 four points 2a + 3b - c, a - 2b + 3c, 3a + 4b -2c and a - 6b + 6c arw coplanar, where a, b, c are no-coplaner
- Prove that the three points -2a + 3b + 5c, a + 2b + 3c and 7a - c are colinear, where a, b, c are non-coplanar
- Show that a is perpendicular to b iff |a + b| = |a - b|.
- 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|?
