IITM BS Question 9 - Week 8 Practice

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IITM BS Question 9 - Week 8 Practice | Prasnya

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Q9Comprehension1 Mark31 Aug 2025

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Based on the above data, answer the given subquestions. Let

f: \mathbb{R}^3 \to \mathbb{R}

be a real-valued function such that

(1/\sqrt{10}, 0, -3/\sqrt{10})

is a direction along which no change in

f

is observed at the point

(1, 1, 1)

. Suppose the gradient of

f

(-1, -1, -1)

exists and is continuous in a ball around

(-1, -1, -1)

and is given by

(-9, b, c)

, where

b, c \in \mathbb{R}

Let S denote the set of all unit directions along which there is no change in f, and which are perpendicular to (1/sqrt(10), 0, -3/sqrt(10)). Find dim(Span{S}).

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31 Aug 2025

Mathematics 2 · Week 8

Q9.Let S denote the set of all unit directions along which there is no change in f, and which are perpendicular to (1/sqrt(10), 0, -3/sqrt(10)). Find dim(Span{S}).@passage

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