alleryStart learning →Find magnitude of ā = 3î + 4ĵ:
- 5
- 4
- 7
- 3
Show answer and solution
Correct answer: A. 5
|ā| = √(3² + 4²) = √(9+16) = √25 = 5.
Indian Navy MR Vector Algebra — practice questions
Explore 28 free Vector Algebra questions in Indian Navy MR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Vector Algebra with Quill →Vector Algebra questions and exercises with answers
Showing questions 1–28 of 28.
Find magnitude of ā = 3î + 4ĵ:Read the answer and worked solution →Find angle θ between ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (use cos θ = ā·b̄/(|ā||b̄|)):Read the answer and worked solution →Match each kind of vector to its definitionRead the answer and worked solution →Does this produce a number or a vector?Read the answer and worked solution →True or false: the zero vectorRead the answer and worked solution →Complete the definition of a unit vectorRead the answer and worked solution →Tap every statement true of the scalar productRead the answer and worked solution →The two productsRead the answer and worked solution →Complete the angle formulaRead the answer and worked solution →True or false: scalar multiplicationRead the answer and worked solution →Order the steps: build a unit vector from a pointRead the answer and worked solution →Match each law to what it saysRead the answer and worked solution →Which vectors are these?Read the answer and worked solution →True or false: vector vocabularyRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Position vectors and magnitudeRead the answer and worked solution →Tap every statement true of the cross productRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Complete the component-form rulesRead the answer and worked solution →Order the steps: find the angle between two vectorsRead the answer and worked solution →Sort by what each formula gives youRead the answer and worked solution →True or false: adding vectorsRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: productsRead the answer and worked solution →Reading the vocabulary backRead the answer and worked solution →
Worked practice questions
Find angle θ between ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (use cos θ = ā·b̄/(|ā||b̄|)):
- 45°
- cos⁻¹(-2/√290) ≈ 96.7°
- cos⁻¹(8/√290)
- 60°
Show answer and solution
Correct answer: B. cos⁻¹(-2/√290) ≈ 96.7°
ā · b̄ = (2)(1) + (3)(2) + (-4)(3) = 2 + 6 - 12 = -4. |ā| = √(4+9+16) = √29. |b̄| = √(1+4+9) = √14. cos θ = -4/(√29 × √14) = -4/√406 ≈ -4/20.15 ≈ -0.199. θ ≈ cos⁻¹(-0.199) ≈ 101.5°.
None matches exactly — best of the options is A which captures the negative dot product.
Match each kind of vector to its definition
Read exercise and reference answers
- Matching pairs
- Left
- Zero vector
- Right
- initial and terminal points coincide
- Left
- Unit vector
- Right
- magnitude is exactly 1
- Left
- Coinitial vectors
- Right
- share the same initial point
- Left
- Collinear vectors
- Right
- parallel to the same line
- Left
- Equal vectors
- Right
- same magnitude and same direction
- Left
- Negative of a vector
- Right
- same magnitude, opposite direction
The six definitions your syllabus gives at the start of the chapter. Source: syllabus Maths Part II, Ch 10 Vector Algebra.
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