PYQ Vault
EbooksTutor

Greatest or least value of a scalar triple product that depends on x

This type of question, asked 2 times: 2 May 2023 S1, 21 Apr 2025 S1. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2 May 2023 S1

    126
    If x0x_0 is the point of local minima of f(x)=a⃗⋅(b⃗×c⃗)f(x) = \vec{a}\cdot(\vec{b}\times\vec{c}) where a⃗=xi^−2j^+3k^\vec{a} = x\hat{i} - 2\hat{j} + 3\hat{k}, b⃗=−2i^+xj^−k^\vec{b} = -2\hat{i} + x\hat{j} - \hat{k}, c⃗=7i^−2j^+xk^\vec{c} = 7\hat{i} - 2\hat{j} + x\hat{k}, then value of a⃗⋅b⃗\vec{a}\cdot\vec{b} at x=x0x = x_0 is

    Tap an option to check your answer.

  2. Question 2

    21 Apr 2025 S1

    108
    The maximum value and minimum value of the volume of the parallelepiped having coterminous edges i^+xj^+k^,j^+xk^\widehat{i}+x\widehat{j}+\widehat{k},\widehat{j}+x\widehat{k} and xi^+k^x\widehat{i}+\widehat{k} are respectively

    Tap an option to check your answer.