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MP Board Class 12 (MPBSE) Vector Algebra — practice questions

Explore 27 free Vector Algebra questions in MP Board Class 12 (MPBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vector Algebra questions and exercises with answers

Showing questions 1–27 of 27.

Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if: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

Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if:

  1. $\vec a + \vec b + \vec c = 0$ on the school chart here
  2. $\vec a\cdot\vec b = \vec b\cdot\vec c = 0$ on the chart all the time
  3. $|\vec a| + |\vec b| = |\vec c|$ on chart at all times
  4. Their scalar triple product $[\vec a\, \vec b\, \vec c] = 0$
Show answer and solution

Correct answer: D. Their scalar triple product $[\vec a\, \vec b\, \vec c] = 0$

Three vectors are coplanar iff their scalar triple product (parallelepiped volume) is zero.

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Match each kind of vector to its definition

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Matching pairs
  1. Left
    Zero vector
    Right
    initial and terminal points coincide
  2. Left
    Unit vector
    Right
    magnitude is exactly 1
  3. Left
    Coinitial vectors
    Right
    share the same initial point
  4. Left
    Collinear vectors
    Right
    parallel to the same line
  5. Left
    Equal vectors
    Right
    same magnitude and same direction
  6. 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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Does this produce a number or a vector?

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Items
  1. Item
    a · b
    Category
    A number (scalar)
  2. Item
    |a|
    Category
    A number (scalar)
  3. Item
    a₁b₁ + a₂b₂ + a₃b₃
    Category
    A number (scalar)
  4. Item
    a × b
    Category
    A vector
  5. Item
    a + b
    Category
    A vector
  6. Item
    λa
    Category
    A vector
Categories
  1. Item
    A number (scalar)
  2. Item
    A vector
The scalar product returns a number the cross product returns a vector perpendicular to both. Getting this backwards is the most expensive mistake in the chapter. Source: syllabus Maths Part II, Ch 10 Vector Algebra.

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