Exams › JEE Main › Maths

Let A = 2î + 3ĵ + 6k̂, B = î + ĵ - 2k̂, and C = î + 2ĵ + k̂. Find the value of |A × [A × (A × B) ] · C |.

1. 343
2. 512
3. 221
4. 243

Correct answer: 343

Solution

The expression involves multiple vector cross products and the dot product, ultimately simplifying to a scalar value. The correct option is derived from the properties of vector operations, specifically the triple product and the magnitudes involved, leading to the final result of 343.

Related JEE Main Maths questions

• If ((â × b̂) × (ĉ × d̂)) · (â × d̂) = 0, which statement must always hold?
• For four points A, B, C and D in space, if the dot product of vectors AB and CD is given by k times [|AD|² + |BC|² - |AC|² - |BD|²], then what is the value of k?
• Three vectors →a, →b and →c have magnitudes |→a| = 4, |→b| = 4 and |→c| = 2. If →a is orthogonal to (→b + →c), →b is orthogonal to (→c + →a), and →c is orthogonal to (→a + →b), then the magnitude of (→a + →b + →c) is:
• The position vectors of the vertices A, B and C of triangle ABC are 4î + 7ĵ + 8k̂, 2î + 3ĵ + 4k̂ and 2î + 5ĵ + 7k̂ respectively. The position vector of the point where the internal bisector of angle A intersects BC is
• Let a=a₁î+a₂ĵ+a₃k̂, b=b₁î+b₂ĵ+b₃k̂, and c=c₁î+c₂ĵ+c₃k̂ be three non-zero vectors. Suppose c is a unit vector perpendicular to both a and b. If the angle between a and b is π/6, then the value of |[a₁, a₂, a₃; b₁, b₂, b₃; c₁, c₂, c₃] | is
• Let a, b, and c be three vectors that are not in the same plane. Define p = (b × c)/([abc]), q = (c × a)/([abc]), and r = (a × b)/([abc]). Then the value of (a+b)·p + (b+c)·q + (c+a)·r is

⚔️ Practice JEE Main Maths free + battle 1v1 →