A, B, C , D are four points in a plane with position vectors a, b, c, d respectively, such that . The point D then is the . . . . . . . of the triangle ABC.
My Self Assessment
a) Orthocentre
Let be unit vectors such that . Which one of the following is correct
a)
b)
c)
d) are mutually perpendicular
Multiple choice
Which of the following expressions are meaningful
d)
Let a and b be two non-collinear unit vectors. If and then is
a) ||
Find all values of λ such that and
where are unit vectors along the coordinate vectors.
If c be a given non-zero scalar and A and B be given non-zero vectors such that A is perpendicular to B, find the vector X which satisfies the equations
The position vectors of the point A, B, C, D are respectively. If the points A, B, C and D lie in a plane, find the value of λ.
Let OABC be a parallelogram with O as the origin and OC a diagonal. Let D be the midpoint of OA. Using vector method, prove that BD and CO intersect in the same ratio.
If a, b, c are coplanar, show that
Let A = . Determine a vector R satisfying and .
Determine the value of c so that for all real x the vector cx and make an obtuse angle with each other.
If a, b, c, d are distinct vectors satisfying relation and . Prove that
Fill in the blank
Let A, B, C be three vectors of length 3, 4, 5 respectively. Let A is perpendicular to B + C, B is perpendicular to C + A, and C is perpendicular to A + B then the length of the vector is equal to . . . .
If A, B, C are three non-coplanar vectors then
If are given vectors then the vector B satisfying the equation and is . . . . .
If the vectors
are coplanar then the value of . . . . . .
The projection of a vector a along and perpendicular to a non-zero vector are . . . . . and . . . . . respectively.
Given that a = (1, 1, 1), c = (0, 1, −1), a . b = 3, then b is equal to
A unit vector coplanar with and and perpendicular to is . . . . .
A unit vector perpendicular to the plane determined by the points P (1, -1, 2), Q (2, 0, -1) and R (0, 2, 1) is . . . . .
A non-zero vector a is parallel to the line of intersection of the plane determined by the vectors and the plane determined by the vectors . The angle between a and is . . . . .
If b and c are any two non-collinear unit vectors and a is any vector then . . . . .
Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If then the acute angle between a and c is . . . . .
Solve
. The point D then is the . . . . . . . of the triangle ABC.
