Success TrackerSuccess Tracker
Log inSign up

GATE EE 2024 Set 1 — Question 36

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
MCQ+2 / -0.67MediumDirectional DerivativesVector CalculusEngineering Mathematics

Engineering Mathematics → Vector Calculus → Directional Derivatives

Last updated

Question

Consider a vector uˉ=2x^+y^+2z^\bar{u} = 2\hat{x} + \hat{y} + 2\hat{z}, where x^,y^,z^\hat{x}, \hat{y}, \hat{z} represent unit vectors along the coordinate axes x,y,zx, y, z respectively. The directional derivative of the function f(x,y,z)=2ln⁡(xy)+ln⁡(yz)+3ln⁡(xz)f(x, y, z) = 2 \ln(xy) + \ln(yz) + 3 \ln(xz) at the point (x,y,z)=(1,1,1)(x, y, z) = (1, 1, 1) in the direction of uˉ\bar{u} is
Your answer

Choose one option, then check your answer.

The solution stays hidden until you check.

Continue learning with Success Tracker

A step still unclear? Work through it with support

Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans
PYQs with solutions
Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts
Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support
Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

Start with a free accountView plans and allowances

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.

More questions on Vector Calculus

2026 Set 1 Q14Consider the following differential equation:…2026 Set 1 Q30Two n×nn \times n matrices AA and BB have a common eigenvalue 22, and the same corresponding…2026 Set 1 Q32Given that F⃗(x,y,z)=sin⁡(y)x^+cos⁡(x)y^+5z^\vec{F}(x, y, z) = \sin(y) \hat{x} + \cos(x) \hat{y} + 5 \hat{z}, the integral…2026 Set 1 Q35AA is an m×mm \times m skew-symmetric matrix with real-valued entries, and xx is an…2026 Set 1 Q36A time-limited waveform g(x)g(x) is specified as follows:…