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Class 10 Mathematics Chapter 6 Full Unit Test | Vectors in Plane | Punjab Board 2027 Model Paper
Class 10 Math Chapter 6 Full Unit Test
Class 10 Mathematics Chapter 6: Vectors in Plane Full Unit Test is prepared according to the Punjab Board 2027 Model Paper pattern. This Class 10 Math Chapter 6 Test covers important questions about vectors, vector magnitude, unit vectors, parallel vectors, position vectors, vector components, triangle law of addition, translation vectors, and applications of vectors. Students can use this Vectors in Plane Full Unit Test for Punjab Board 2027 exam preparation and practice.
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Full Unit Test
Unit 6: Vectors in Plane
Board Paper Pattern 2027
Objective Type
Time Allowed: 20 Min.
Max. Marks: 15
Note: Four possible answer A, B, C and D to each question are given.
The choice which you think is correct, fill that circle front of that
question with Marker or ink pen in the answer book. Cutting filling
two or more circles will result in zero mark in that question.
(i) Which of the following is not a vector quantity?
(ii) Magnitude of the vector
a = i + 2j
is |a| =
(iii) Which of the following is a unit vector?
(iv) If a = −2i + j
then 3a =
(v) If a = i − 3j
then which of the following has opposite direction to that of a?
(vi) If a is a unit vector then |a| =
(vii) The point (−4, −4) lies in the ______ quadrant.
(viii) If A(8, 0), B(−8, 0) then |AB| =
(ix) If a = 4i − 2j
then a vector having double the magnitude that of a
and same direction is:
(x) Which of the following represents Triangle Law of Addition of vectors?
(xi) If a = 3i − 4j
and b = 5i + 4j
then b − a =
(xii) x-axis and y-axis divide a coordinate plane into ______ parts.
(xiii) The point (−1, 1) lies in ______ quadrant.
(xiv) Translation vector shows:
(xv) A ball is projected with velocity vector
V = 6i + 8j,
then magnitude of the velocity is:
Here is
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Subjective Type
Time Allowed: 2:10 hours
(Part-I)
Max. Marks: 60
2. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) If P(2, 4) and Q(−5, 3), then find
(i) PQ in the form
xi + yj
(ii) |PQ|
(ii) If P(4, 7) and Q(5, 10), then find the magnitude of the vector
PQ.
(iii) If a = 3b, where
a = 9i − kj and
b = 3i − 12j, then find the value of k.
(iv) Show that
a = 5i − 2j and
b = −10i + 4j
are parallel.
(v) Find a unit vector in the direction of
a = −5i + 2j.
(vi) If a is a unit vector, then what is the value of
|a|?
(vii) Name the quadrant in which each point lies: (−4, −4)
(viii) Write the vector AB in the form of
xi + yj:
A(8, 9), B(12, 3)
(ix) Find a unit vector in the direction of given vector:
a =
1/√6 i +
1/√6 j
3. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) Find a unit vector in the direction of the vector given below:
a = −4i + 5j.
(ii) Which of the following vectors are parallel?
a = 6i + j,
b = 12i + 2j.
(iii) Define position vector.
(iv) Plot the following points on the coordinate plane:
C(5, 7).
(v) Define zero vector.
(vi) Define magnitude of a vector.
(vii) Find a unit vector thrice in length of
3i − 2j,
but opposite in direction.
(viii) Define Triangle Law of Addition.
(ix) If a = 2i − 3j and
b = 3i + 4j, then find the vector components of
3a + 4b.
4. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) If a = 7i − 3j and
b = i + 5j, then find the following vectors:
¾a − b.
(ii) If a = 6i − j,
b = i + 5j and
c = 3i + 5j, then find the magnitudes of
the following vectors: b − c.
(iii) Find the values of x and
y in each of the following equations:
(xi + yj) + (2i + 3j) = 7i + 6j.
(iv) If a = −2i + 7j and
b = 3i − 5j, then find the vector components of
a + 5b.
(v) If A(1, 2), B(4, 6) and C(7, 2) are the vertices of triangle.
Check whether triangle ABC is an isosceles.
(vi) Use vector method, to show that the points
A(1, 2), B(4, 6), C(7, 4) and D(4, 0) form a parallelogram.
(vii) A projectile is launched from ground with initial velocity vector
12i + 16j. After how long does it hit a target
located 24 metres away horizontally?
(viii) A tank fires a shell with velocity vector
V₁ = 30i + 40j at a moving target heading east at
V₂ = 10i + 0j.
Find relative velocity and its magnitude.
(ix) A car enters a loop with velocity vector
v = 30i and exits with velocity
v′ = 30i.
What is the change in velocity vector?
(Part-II)
Note: Attempt any two (02) questions.
(2 × 8 = 16)
5:(a)
If a = 5i − 7j,
b = −i − j and
c = 2i + 3j, then find unit vector parallel to
a + b − 3c.
(b)
Find two vectors that are double in magnitude of
3i − 5j, one in the same direction of it
and other in its opposite direction.
6:(a)
If a = i + 3j,
c = 2i + j and
a + 2b = c, then find |b|.
(b)
If
5i − 3j = m(i − 10j) + n(4i − 3j),
then find the values of m and n.
7:(a)
Plot A(−4, 2), B(−1, 2) and C(−3, 4) to form a triangle ABC.
Also translate ΔABC to ΔA′B′C′ by the translation vector
7i + 2j.
(b)
Plot A(−6, 3), B(−4, 0), C(−2, 3) and D(−4, 4) to form a kite ABCD.
Also translate kite ABCD to kite A′B′C′D′ by translation vector
6i − 6j.
(Part-III)
Note: Attempt any one (01) question.
(1 × 8 = 8)
8:(a)
In parallelogram ABCD, the vectors representing two opposite sides are
AB = 6i + 2j,
DC = −6i − 2j.
Show that the opposite sides are equal in magnitude and parallel.
(b)
Find the values of x and
y in the following equation:
(2xi + yj) + (−i + 5j)
= 1/4i − 8j
.
9:(a)
Use vectors to show that ABCD is a parallelogram, where the points are
A(2,3), B(6,3), C(7,6) and D(3,6).
(b)
Use vectors to show that triangle ABC is an isosceles triangle,
where the points A, B and C have coordinates
(1, 2), (4, 6) and (7, 2) respectively.
