AKUEB HSSC-I Mathematics Vectors MCQs & Practice Questions

Class 11 - Mathematics / Unit 11 - Vectors / 11.2 Vectors in Space / 11.2.4

AKU-EB Model Paper 2025MEDIUM

Fill in the blank:

The vectors

\mathbf{P}

\mathbf{Q}

and

\mathbf{R}

are given as

\mathbf{P}=2\mathbf{i}-3\mathbf{j}+4\mathbf{k}

\mathbf{Q}=\mathbf{j}-\mathbf{k}

and

\mathbf{R}=3\mathbf{i}-\mathbf{k}

.
Note: Answer the blanks using the built in math tool. i. Show that the magnitude of

\mathbf{P}-5\mathbf{Q}

\sqrt{149}

units.

\mathbf{P}-5\mathbf{Q}=

, that has magnitude 149. ii. Find the unit vector in the direction of

\mathbf{P}-5\mathbf{Q}

. It has:

\mathbf{i}

-component:

\mathbf{j}

-component:

\mathbf{k}

-component:
iii. State a vector which is parallel to the vector

\mathbf{R}

but opposite in direction.
That vector with all components is:

Class 11 - Mathematics / Unit 11 - Vectors / 11.5 Scalar Triple Product / 11.5.3

AKU-EB Model Paper 2025MEDIUM

While evaluating a scalar triple product involving standard unit vectors, a student claims that $\hat{j}\cdot(\hat{i}\times\hat{k})=1$ based on their understanding of vector products. Based on the given situation, the TRUE option will be

Correct - result equals

1

Incorrect - result equals

-1

Correct - dot product

1

of all unit vectorsIncorrect - cross product zero

Class 11 - Mathematics / Unit 11 - Vectors / 11.4 Cross or Vector Product / 11.4.6

AKU-EB Model Paper 2025HARD

Which of the following statements is CORRECT for $\overrightarrow{A}-2\overrightarrow{B}=\overrightarrow{0}$ and $\overrightarrow{C}+3\overrightarrow{A}=\overrightarrow{0}$ ? (Note: $\overrightarrow{A}$ , $\overrightarrow{B}$ , and $\overrightarrow{C}$ are non-zero vectors and $\overrightarrow{0}$ is a zero vector.)
I. Vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are parallel and have opposite directions.
II. Vectors $\overrightarrow{A}$ and $\overrightarrow{C}$ are parallel and have same directions.
III. Vectors $\overrightarrow{A}$ , $\overrightarrow{B}$ and $\overrightarrow{C}$ are parallel to each other.

I onlyIII onlyI and IIII and III

Class 11 - Mathematics / Unit 11 - Vectors / 11.3 Dot or Scalar Product / 11.3.5

AKU-EB Model Paper 2025MEDIUM

If $\overrightarrow{A}\cdot\overrightarrow{B}=0$ , then $\overrightarrow{A}$ and $\overrightarrow{B}$ must be perpendicular and unit vectors. Which of the following options justifies the given statement?

True - Vectors are unit and perpendicular because their dot product is zero.False - Vectors are perpendicular only because their dot product is zero.True - Only unit vectors are perpendicular because their dot product is one.False - Only vectors are perpendicular because their dot product is one.

Class 11 - Mathematics / Unit 11 - Vectors / 11.1 Vectors in a Plane / 11.1.5

AKU-EB Model Paper 2025MEDIUM

The geometrical representation of vector $\overrightarrow{KL}$ is shown in a diagram. The vector $\overrightarrow{KL}$ will be

-\mathbf{i}+2\mathbf{j}

\mathbf{i}+3\mathbf{j}

-3\mathbf{i}+2\mathbf{j}

2\mathbf{i}-3\mathbf{j}

Class 11 - Mathematics / Unit 11 - Vectors / 11.2 Vectors in Space / 11.2.7

AKU-EB Model Paper 2025HARD

A student is designing a drone's flight path. First, it will move $5$ m East (vector $\overrightarrow{A}$ ), then $3$ m North (vector $\overrightarrow{B}$ ). Another student suggests reversing the steps: first $3$ m North, then $5$ m East.
If the student follows the reversed path (North then East), then the final position compared to the original path will

follow the same trajectoryfollow a curved pathend up at the same position due to commutative propertyend up at the same position due to associative property

Vectors - HSSC-I Mathematics