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JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Vector Algebra

Let

a = 3 \hat{i} + \hat{j}

and

b = \hat{i} + 2 \hat{j} + \hat{k}

. Let

c

be a vector satisfying

a \times (b \times c) = b + λ c

. If

b

and

c

are non-parallel, then the value of

λ

is :

(A)-5✓ Correct
(B)5
(C)1
(D)-1

Answer: (A)

Solution

Using the vector triple product identity:

a \times (b \times c) = (a \cdot c) b - (a \cdot b) c

Given:

(a \cdot c) b - (a \cdot b) c = b + λ c

Comparing coefficients:

a \cdot c = 1

and

- (a \cdot b) = λ

Calculating:

a \cdot b = (3 \hat{i} + \hat{j}) \cdot (\hat{i} + 2 \hat{j} + \hat{k}) = 3 + 2 = 5

Therefore:

λ = - 5

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Single correct option

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