JEE-Main - Grade 12 - Mathematics - Vector Algebra - Introduction and Snapshot of Vector Algebra - Study ref# 926

Introduction
In our day to day life, we come across
many queries such as – What is your height? How should a football player hit the
ball to give a pass to another player of his team? Observe that a possible
answer to the first query may ... read more

JEE-Main - Grade 12 - Mathematics - Vector Algebra - Introduction and Snapshot of Vector Algebra - Study ref# 927

Following sections must be covered to
understand the Vector Algebra:
1. Some Basic Concepts
2. Types of Vectors
3. Addition of Vectors
4. Multiplication of a Vector by a Scalar
5. Product of Two Vectors... read more

JEE-Main - Grade 12 - Mathematics - Vector Algebra - Target Setup for Vector Algebra - Study ref# 928

Student requires to achieve the following milestones to get better grip over Vector Algebra. The milestones / targets are as follows: Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test000%... read more

Represent graphically a displacement of
40 km, 30° east of north. Answer: The displacement is 30°
east of north so, we have to draw a straight line making 30°
with north.
Here, vector OP represent the
dis... read more

Classify the following measures as
scalars and vectors:
(i) 10 kg (ii) 2 m north
– west (iii) 40°
(iv) 40 W (v) (vi)
20 m/s2 Answer: (i) Scalar Here th... read more

Write two differential vectors having
same magnitude. Answer: Two vectors can have same magnitude, if
the sum of the squares of coefficient of and is same. Let vectors and are different vec... read more

Write two different vectors having same
direction.
Hints – The vectors can have the same
directions, if their direction cosines (l, m, n) are same. Direction cosines
for a vector A = are
given by Answer: Let read more

Find the scalar and vector components of
the vector with initial point (2,1) and terminal point (-5,7).
Hints- A vector initial point and final point is given . Answer: Vector with initial point A(2,1) and
final (terminal) point B(- 5, 7)... read more

Find the unit vector in the direction of
the vector .
Hints – Unit vector in the direction of
given vector can be calculated by formula where, magnitude of given vector
a. Answer: Gi... read more

Find the unit vector in the direction of
vector PQ, where P and Q are the points (1,2,3) and (4,5,6), respectively.
Hints – In the question we are not given
the vector, so first of all vector is to be calculated and then find the unit
vec... read more

Find the direction cosines of the vector
joining the points A(1,2,-3) and B(-1,-2,1), directed from A to B. Answer: The given points are A(1,2,-3) and
B(-1,-2,1).
i.e., and
Vector AB ... read more

Find the position vector of the mid-point
of the vector joining points P(2,3,4) and Q(4,1,-2). Answer: The position vector of mid-point of the
vector joining the points P(2,3,4) and Q(4,1,-2) is given by
PV of the mid – point of (PQ) = (PV ... read more

Show that the points A,B and C with
position vectors, and respectively, form the
vertices of a right angled triangle.
Hints – If three points A,B,C form a
right angle triangle, then
read more

Find the angle between two vectors a
and b with magnitude and
2 respectively, having .
Hints – To determine the angle between a
and b, we can use the formula
Answer: It is given ... read more

Find the projection of vector on the vector .
Hints – Use formula for projection of a
on b = Answer: Let a = and b=
Projection of a and b is
given by
Hence, the projection of ... read more

If a, b, c are unit
vectors such that a+ b+ c=0, then find the value of
Hints – As a, b and c are
unit vectors, so use and expand to get the value of Answer: Given , if and
Hints – Suppose , and , then use
. ... read more

Write down a unit vector in XY –plane,
making an angle of 30° in anticlockwise direction with the positive direction of X
–axis. Answer: Let OP makes 30° with
X-axis , 60° with Y-axis and 90° with Z-a... read more

A girl walks 4km towards west then, she
walks 3km in a direction 30° east of north and stops. Determine the girl’s displacement from
her initial point of departure. Answer: Let O and B be the initial and final
position... read more

The two adjacent sides of a parallelogram
are and . Find the unit vector
parallel to its diagonal. Also, find its area. Answer: Adjacent sides of a parallelogram are
given as and .
Then , the diagonal ... read more

A plane electromagnetic wave of frequency
25 MHz travels in free space along the x=direction. At a particular point in
space and time, .What
is B at this point? Answer: The magnitude of B is
... read more