GATE CS 2017 Set 1 — Question 30
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumVector Spaces & Linear MapsLinear AlgebraEngineering Mathematics
Engineering Mathematics → Linear Algebra → Vector Spaces & Linear Maps
Last updated
Question
Let and be two vectors in whose Euclidean norms satisfy . What is the value of such that bisects the angle between and ?
Correct answer
(A) 2
Solution
The angle bisector of two vectors and lies along the direction of the sum of the unit vectors of and . That is, the bisector is parallel to:
We are given that bisects the angle. Therefore, must be a scalar multiple of the vector above:
Given , let , then . Substituting these values:
Comparing the coefficients of and :
Coefficient of :
Coefficient of : Substitute into the equation for :
Thus, .
We are given that bisects the angle. Therefore, must be a scalar multiple of the vector above:
Given , let , then . Substituting these values:
Comparing the coefficients of and :
Coefficient of :
Coefficient of : Substitute into the equation for :
Thus, .
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 CS 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.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Linear Algebra
2026 Set 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…