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Federal (FBISE) · Chapter test · Free

10th Class Mathematics Chapter 7 Test07. Vectors in Plane

30 marks · 40 minutes · 21 questions. Covers: 07. Vectors in Plane.

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10th Class Mathematics Chapter 7 Test

10th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. Which of the following vectors represents a position vector?
    1. OP→\overrightarrow{OP}
    2. −OP→-\overrightarrow{OP}
    3. PO→\overrightarrow{PO}
    4. PQ→\overrightarrow{PQ}
  2. Given that u⃗\vec{u} is any vector. Which of the following is true?
    1. ∣−u⃗∣=∣u⃗∣\left| -\vec{u} \right| = \left| \vec{u} \right|
    2. −∣u⃗∣=∣u⃗∣-\left| \vec{u} \right| = \left| \vec{u} \right|
    3. ∣u⃗∣=∣−u⃗∣\left| \vec{u} \right| = \left| -\vec{u} \right|
    4. ∣u⃗∣=0| \vec{u}| = 0
  3. If OP→\overrightarrow{OP}= [-6 , 7] , then −OP→-\overrightarrow{OP} is equal to
    1. [-6 , 7]
    2. [6 , 7]
    3. [6 , -7]
    4. [-6 , -7]
  4. If u⃗=[−5x,8]\vec{u} = [-5x , 8] and v⃗=[10,4y]\vec{v} = [10 , 4y] are equal vectors, then:
    1. x = 2 , y = 2
    2. x = -2 , y = -2
    3. x = -2 , y = 2
    4. x = 2 , y = -2
  5. The unit vector of the vector u⃗=6i^+10j^−2j^\vec{u} = 6\hat{i} + 10\hat{j} - 2\hat{j} is:
    1. 3i5−4j5 \frac{3i}{5} - \frac{4j}{5}
    2. 3i5+4j5 \frac{3i}{5} + \frac{4j}{5}
    3. −3i5−4j5 -\frac{3i}{5} - \frac{4j}{5}
    4. b) −3i5+4j5 -\frac{3i}{5} + \frac{4j}{5}
  6. u⃗=5i^+10j^ and v⃗=4j^, then ∣u⃗−v⃗∣ is\vec{u} = 5\hat{i} + 10\hat{j} \text{ and } \vec{v} = 4\hat{j}, \text{ then } |\vec{u} - \vec{v}| \text{ is}
    1. 123\sqrt{123}
    2. 61\sqrt{61}
    3. 11\sqrt{11}
    4. −61-\sqrt{61}
  7. Which of the following is a vector quantity?
    1. velocity
    2. speed
    3. distance
    4. work
  8. If a⃗\vec{a} and b⃗\vec{b} are position vectors of points A and B respectively, then AB→\overrightarrow{AB} is
    1. b⃗\vec{b} +a⃗\vec{a}
    2. a⃗\vec{a} - b⃗\vec{b}
    3. b⃗\vec{b} - a⃗\vec{a}
    4. −b⃗-\vec{b} - a⃗\vec{a}
  9. What type of a quadrilateral ABCD is, if AB→=23DC→?\overrightarrow{AB} = \frac{2}{3} \overrightarrow{DC}?
    1. kite
    2. rectangle
    3. trapezium
    4. rhombus
  10. If p⃗\vec{p} = [5 , -6] and q⃗\vec{q} = [2 , 6], then is:
    1. [1 , -18]
    2. [9 , 18]
    3. [1 , 18]
    4. [-9 , -18]

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Draw vectors a⃗\vec{a} = 3 units west and b⃗\vec{b} = 3 unit north on graph paper. Draw the following vector on the graph paper. a⃗−2b⃗\vec{a} - 2\vec{b}
  2. Find the unit vector of the following vector. b⃗=−6i^−8j^\vec{b}= -6\hat{i}- 8\hat{j}
  3. P(3 , - 4) is a point in the plane. Find the position vectorOP→\overrightarrow{OP} and then its negative vector.
  4. Given that OP→=p⃗+q⃗\overrightarrow{OP} = \vec{p} + \vec{q}, OQ→=p⃗−q⃗\overrightarrow{OQ} = \vec{p} - \vec{q} and M is mid-point of PQ→\overrightarrow{PQ}. Find in term of p⃗\vec{p} and q⃗\vec{q}. OP→=p⃗+q⃗,OQ→=p⃗−q⃗\overrightarrow{OP} = \vec{p} + \vec{q}, \quad \overrightarrow{OQ} = \vec{p} - \vec{q} and M is mid-point of PQ→\overrightarrow{PQ}.
  5. Draw vectors a⃗\vec{a} = 3 units west and b⃗\vec{b} = 3 unit north on graph paper. Draw the following vector on the graph paper. 0.5(a⃗+b⃗)0.5(\vec{a} +\vec{b} )
  6. If and = [1 , 3], then find a unit vector in the direction of:If a⃗=2i^−4j^\vec{a} = 2\hat{i} - 4\hat{j}, b⃗=i^−2j^\vec{b} = \hat{i} - 2\hat{j} and c⃗=[1,3]\vec{c} = [1, 3], then find a unit vector in the direction of: 2a⃗−b⃗2\vec{a} - \vec{b}
  7. In △OAB\triangle OAB, OA→=a⃗\overrightarrow{OA} = \vec{a}, OB→=b⃗\overrightarrow{OB} = \vec{b} and M is mid-point of OA→\overrightarrow{OA}. Write the following vectors in terms of a⃗ and b⃗.BM→\vec{a} \text{ and } \vec{b} . \overrightarrow{BM}Question diagram
  8. Find the unit vector of the following vector. PQ→\overrightarrow{PQ} when P (1 , 4) , Q (4 , 8)

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. A truck leaves dry port on a bearing of 30° and travels 15 km. It then turns due west and travels 8 km. How far is the truck from the dry port and what is its bearing?
  2. Prove that the line segments joining the midpoints of two sides of a triangle are half in length of third side.
  3. Prove that the joining the midpoints of the two non-parallel sides of a trapezium is parallel to its parallel sides.