For three vectors A = (-xî - 6ĵ - 2k̂), B = (-î + 4ĵ + 3k̂) and C = (-8î - ĵ + 3k̂), if A · (B × C) = 0, then value of x i s _________.
Physics · Mathematical tools and vector
JEE Mains 2024 06 Apr Morning Shift

Question

For three vectors A = (-xî - 6ĵ - 2k̂), B = (-î + 4ĵ + 3k̂) and C = (-8î - ĵ + 3k̂), if A · (B × C) = 0, then value of x i s _________.

G1 Physics · Accepted Answer

Given: B = -î + 4ĵ + 3k̂ C = -8î - ĵ + 3k̂ Cross product: B × C = | î ĵ k̂ | |-1 4 3 | |-8 -1 3 | = 15î - 21ĵ + 33k̂ Now: A = -xî - 6ĵ - 2k̂ Given: A · (B × C) = 0 Therefore: (-x)(15) + (-6)(-21) + (-2)(33) = 0 -15x + 126 - 66 = 0 -15x + 60 = 0 x = 4