Basics of Vectors: JEE Questions & Solutions

Let the arc AC of a circle subtend a right angle at the center O. If the point B on the arc AC divides the arc AC such that: length of arc…

Let the position vectors of the vertices A, B, and C of a tetrahedron ABCD be i + 2 j + k, i + 3 j - 2 k, and 2 i + j - k respectively. The…

Let a = i + 2 j + 3 k, b = 3 i + j - k and c be three vectors such that c is coplanar with a and b. If the vector c is perpendicular to b…

Let the position vectors of three vertices of a triangle be p = 4 i + j - 3 k, q = -5 i + 2 j + 3 k, and r = -5 i + 3 j + 2 k. Then + 2 + 5…

If the components of a = i + j + k along and perpendicular to b = 3 i + j - k respectively are 1611 (3 i + j - k) and 111 (-4 i - 5 j - 17…

Let the three sides of a triangle ABC be given by the vectors 2 i - j + k, i - 3 j - 5 k, and 3 i - 4 j - 4 k. Let G be the centroid of the…

Let a and b be the vectors of the same magnitude such that | a + b | + | a - b || a + b | - | a - b | = 2 + 1. Then | a + b |^2| a |^2 is:

Let a = i + 2 j + k and b = 2 i + j - k. Let c be a unit vector in the plane of the vectors a and b and perpendicular to a. Then such a…

The position vectors of the vertices A, B, and C of a triangle are A = 2 i - 3 j + 3 k, B = 2 i + 2 j + 3 k, and C = - i + j + 3 k…

Let the position vectors of vertices A, B, and C of a triangle be 2 i + 2 j + k, i + 2 j + 2 k, and 2 i + j + 2 k respectively. Let l1, l2,…

Let a, b, and c be three non-zero vectors such that b and c are non-collinear. If a + 5 b is collinear with c, b + 6 c is collinear with a,…

Let O be the origin and the position vectors of A and B be 2 i + 2 j + k and 2 i + 4 j + 4 k, respectively. If the internal bisector of AOB…

If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the point (3, 2, 1) and parallel to the planes x + 2y + z…

The vector a = - i + 2 j + k is rotated through a right angle, passing through the y-axis in its way, and the resulting vector is b. Then…

The foot of the perpendicular from the point (2, 0, 5) on the line x+12 = y-15 = z+1-1 is (,,). Then, which of the following is NOT correct?

If the points P and Q are respectively the circumcenter and the orthocenter of a ABC, the PA + PB + PC is equal to:

For any vector a = a1 i + a2 j + a3 k, with 10 | a | < 1, i = 1, 2, 3, consider the following statements:

Let ABCD be a quadrilateral. If E and F are the midpoints of the diagonals AC and BD respectively and ( AB- BC)+( AD- DC)=k FE then k is…