[a + b,\ b + c,\ a + b + c] is equal to

The correct answer is Option (4) → \([\vec{a}, \vec{b}, \vec{c}]\)

A scalar triple product does not change when a multiple of one vector is subtracted from another, just as a determinant does not change under such a row operation.

Subtracting the first vector from the third, \((\vec{a} + \vec{b} + \vec{c}) - (\vec{a} + \vec{b}) = \vec{c}\):

    \([\vec{a} + \vec{b},\ \vec{b} + \vec{c},\ \vec{a} + \vec{b} + \vec{c}] = [\vec{a} + \vec{b},\ \vec{b} + \vec{c},\ \vec{c}]\)

Subtracting the third from the second, \((\vec{b} + \vec{c}) - \vec{c} = \vec{b}\):

    \( = [\vec{a} + \vec{b},\ \vec{b},\ \vec{c}]\)

Subtracting the second from the first:

    \( = [\vec{a},\ \vec{b},\ \vec{c}]\)

Note: This topic was not in the CUET 2026 syllabus.