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 + 2j + k, i + 3j - 2k, and 2i + j - k respectively. The…

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

Let the position vectors of three vertices of a triangle be 4p + q - 3r, -5p + q + 2r and 2p - q + 2r. If the position vectors of the…

If the components of a = α i + β j + γ k along and perpendicular to b = 3i + j - k respectively are 16/11 (3i + j - k) and 1/11 (-4i - 5j -…

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

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 = 2i - 3j + 3k, B = 2i + 2j + 3k, and C = -i + j + 3k respectively. If…

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

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

Let O be the origin and the position vectors of A and B be 2i + 2j + k and 2i + 4j + 4k, 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 + 2j + k is rotated through a right angle, passing through the y-axis in its way, and the resulting vector is b. Then the…

The foot of the perpendicular from the point (2, 0, 5) on the line (x+1)/2 = (y-1)/5 = (z+1)/(-1) is (α, β, γ). Then, which of the…

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 |aᵢ| < 1, i = 1, 2, 3, consider the following statements: (A) max { |a₁|, |a₂|, |a₃| } ≤ |a|…

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 equal…