MereTeacher

JEE • NEET • FOUNDATION

JEE Previous Year Question

$If a = (1, 2, 3), b = (2, - 1, 1), c = (3, 2, 1) and a \times (b \times c) = α a + β b + γ c, then$

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.

A $α = 1, β = 10, γ = 3$
B $α = 0, β = 10, γ = - 3$
C $α + β + γ = 8$
D $α = β = γ = 0$

Correct answer: B

Solution

(b) : a \times (b \times c) = α a + β b + γ c (a \cdot c) b - (a \cdot b) c = α a + β b + γ c Comparing like coefficients, we get α = 0, β = a \cdot c = 3 + 4 + 3 = 10, γ = - (a \cdot b) = - (2 - 2 + 3) = - 3

More Vector Algebra PYQs

$If the volume of the tetrahedron formed by the coterminous edgcs a, b and c is 4 , then the volume of the parallelopip\dots$
$The set of all α, for which the vectors a = αt i + 6 j - 3 k and b = t i - 2 j - 2 αt k are inclined at an obtuse angle\dots$
$Let a, b, c be three-unit vectors satisfying\dots$
$Let a = i + x j + k, b = i + j + k, and | a + b | = | a | + | b | then$
$If cos α, cos β, cos γ are the direction cosines of a ve\dots$