krit.club logo

Vectors

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Concept of Vectors and Scalars

Subtopic

Concept of Vectors and Scalars under Vectors for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Which of the following physical quantities is NOT a vector?

    A.

    Displacement

    B.

    Acceleration

    C.

    Work

    D.

    Force

  2. 2.

    According to the triangle law of addition, if PQ⃗\vec{PQ} and QR⃗\vec{QR} are two vectors, their sum is:

    A.

    RP⃗\vec{RP}

    B.

    PR⃗\vec{PR}

    C.

    QP⃗\vec{QP}

    D.

    0⃗\vec{0}

  3. 3.

    The direction ratios of the vector j^\hat{j} are:

    A.

    (1, 0, 0)

    B.

    (0, 1, 0)

    C.

    (0, 0, 1)

    D.

    (1, 1, 1)

Download the worksheet for Vectors - Concept of Vectors and Scalars to practice offline. It includes additional chapter-level practice questions.

Types of Vectors and Vector Operations

Subtopic

Types of Vectors and Vector Operations under Vectors for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the direction of the vector −3k^-3\hat{k}?

    A.

    Along the positive zz-axis

    B.

    Along the negative zz-axis

    C.

    Along the positive xx-axis

    D.

    Along the negative yy-axis

  2. 2.

    If a⃗=3i^−4j^\vec{a} = 3\hat{i} - 4\hat{j}, what is its magnitude?

    A.

    7

    B.

    1

    C.

    5

    D.

    25

  3. 3.

    Which of the following is true for the direction cosines of a vector?

    A.

    l+m+n=1l+m+n = 1

    B.

    l2+m2+n2=0l^2+m^2+n^2 = 0

    C.

    l2+m2+n2=1l^2+m^2+n^2 = 1

    D.

    l2+m2+n2=−1l^2+m^2+n^2 = -1

Download the worksheet for Vectors - Types of Vectors and Vector Operations to practice offline. It includes additional chapter-level practice questions.

Direction Cosines and Direction Ratios

Subtopic

Direction Cosines and Direction Ratios under Vectors for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If a line makes an angle of 180∘180^\circ with the XX-axis, its direction cosine ll is:

    A.

    1

    B.

    0

    C.

    -1

    D.

    12\frac{1}{2}

  2. 2.

    Find the direction ratios of the vector a⃗=6i^+2j^+3k^\vec{a} = 6\hat{i} + 2\hat{j} + 3\hat{k}.

    A.

    (6, 2, 3)

    B.

    (67,27,37)(\frac{6}{7}, \frac{2}{7}, \frac{3}{7})

    C.

    (6, -2, 3)

    D.

    (3, 1, 1.5)

  3. 3.

    If a line is perpendicular to the YY-axis, its direction cosine mm is:

    A.

    1

    B.

    0

    C.

    -1

    D.

    Not defined

Download the worksheet for Vectors - Direction Cosines and Direction Ratios to practice offline. It includes additional chapter-level practice questions.

Scalar (Dot) Product of Vectors

Subtopic

Scalar (Dot) Product of Vectors under Vectors for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the angle between the vector a⃗\vec{a} and the vector 5a⃗5\vec{a} (where a⃗≠0⃗\vec{a} \neq \vec{0})?

    A.

    0∘0^\circ

    B.

    90∘90^\circ

    C.

    180∘180^\circ

    D.

    None of these

  2. 2.

    If a⃗=i^+j^\vec{a} = \hat{i} + \hat{j}, find the value of a⃗⋅a⃗\vec{a} \cdot \vec{a}.

    A.

    1

    B.

    2

    C.

    2\sqrt{2}

    D.

    0

  3. 3.

    The expression a⃗⋅b⃗∣a⃗∣∣b⃗∣\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|} represents:

    A.

    sin⁡θ\sin \theta

    B.

    cos⁡θ\cos \theta

    C.

    tan⁡θ\tan \theta

    D.

    Projection of a⃗\vec{a} on b⃗\vec{b}

Download the worksheet for Vectors - Scalar (Dot) Product of Vectors to practice offline. It includes additional chapter-level practice questions.

Vector (Cross) Product of Vectors

Subtopic

Vector (Cross) Product of Vectors under Vectors for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The value of (a⃗×b⃗)⋅(a⃗+b⃗)(\vec{a} \times \vec{b}) \cdot (\vec{a} + \vec{b}) is:

    A.

    ∣a⃗∣2+∣b⃗∣2|\vec{a}|^2 + |\vec{b}|^2

    B.

    0

    C.

    ∣a⃗×b⃗∣|\vec{a} \times \vec{b}|

    D.

    1

  2. 2.

    If (a⃗×b⃗)⋅c⃗=0(\vec{a} \times \vec{b}) \cdot \vec{c} = 0, then the vectors a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are:

    A.

    Mutually perpendicular

    B.

    Coplanar

    C.

    Collinear

    D.

    Unit vectors

  3. 3.

    If a⃗×b⃗\vec{a} \times \vec{b} is a unit vector, then ∣a⃗∣∣b⃗∣sin⁡θ|\vec{a}||\vec{b}|\sin\theta must be:

    A.

    0

    B.

    1

    C.

    −1-1

    D.

    n⃗\vec{n}

Download the worksheet for Vectors - Vector (Cross) Product of Vectors to practice offline. It includes additional chapter-level practice questions.

Projection of a Vector on a Line

Subtopic

Projection of a Vector on a Line under Vectors for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the scalar projection of the vector a⃗=i^\vec{a} = \hat{i} on the vector b⃗=j^+k^\vec{b} = \hat{j} + \hat{k}.

    A.

    0

    B.

    1

    C.

    12\frac{1}{\sqrt{2}}

    D.

    2\sqrt{2}

  2. 2.

    The scalar projection of a⃗=3i^+4j^+12k^\vec{a} = 3\hat{i} + 4\hat{j} + 12\hat{k} on itself is:

    A.

    13

    B.

    169

    C.

    1

    D.

    0

  3. 3.

    The scalar projection of a⃗=2i^+2j^+k^\vec{a} = 2\hat{i} + 2\hat{j} + \hat{k} on itself is:

    A.

    33

    B.

    99

    C.

    11

    D.

    00

Download the worksheet for Vectors - Projection of a Vector on a Line to practice offline. It includes additional chapter-level practice questions.

Vectors - ICSE Class 12 Maths Notes & Revision | Krit.club