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JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Vector Algebra

Let

c

be a vector perpendicular to the vectors

a = \hat{i} + \hat{j} - \hat{k}

and

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

. If

c \cdot (\hat{i} + \hat{j} + 3 \hat{k}) = 8

then the value of

c \cdot (a \times b)

is equal to ______

Answer: 28

Solution

Perpendicularity to both

a

and

b

makes

c = λ (a \times b)

, and

a \times b = \hat{i} 11 \hat{j} 12 \hat{k} - 1 1 = 3 \hat{i} - 2 \hat{j} + \hat{k}

The condition

c \cdot (\hat{i} + \hat{j} + 3 \hat{k}) = 8

gives

λ (3 - 2 + 3) = 8

, so

λ = 2

and

c = 6 \hat{i} - 4 \hat{j} + 2 \hat{k}

. Hence

c \cdot (a \times b) = λ a \times b^{2} = 2 (9 + 4 + 1) = 28

so

c \cdot (a \times b) = 28

.

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Integer answer

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