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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 ...
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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...
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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%...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9585
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...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9586
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...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9587
Compute the magnitude of the following vectors:
Hints – The magnitude for a vector is given by Answer: Given, vector
. Comparing...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9588
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...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9589
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
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9590
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)...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9591
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...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9592
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...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9593
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 ...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9594
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 ...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9595
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
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9596
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 ...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9597
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 ...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9598
Find
and , if and =8. Answer: Given,
and =8
 ...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9599
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
. ...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9602
Show that
. Answer: Given that
LHS =
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9603
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...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9604
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...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9605
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 ...
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JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9606
If
, show that . Interpret the result geometrically? Answer:
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JEE-Main - Grade 12 - Physics - Electromagnetic Waves - Study ref# 10592
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 ...
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