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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 ... 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

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... read more

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... read more

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... read more

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... read more

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 read more

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)... read more

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... read more

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... read more

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 ... read more

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 ... read more

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 read more

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 ... read more

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 ... read more

JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9598

Find  and  , if  and =8. Answer: Given,  and =8     ... read more

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  . ... read more

JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9602

Show that  . Answer: Given that   LHS =              read more

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... read more

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... read more

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 ... read more

JEE-Main - Grade 12 - Mathematics - Vector Algebra - Study ref# 9606

If , show that . Interpret the result geometrically? Answer:     read more

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                                            ... read more

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