NCERT solutions for Class 12 Maths Chapter 10 are explained in a detailed manner to help students prepare for their board exam and competitive exams. Important topics that are Maths Vector Questions And Solutions 8th going to be discussed in class 12 Maths Chapter 10 NCERT solutions are vector quantities, operations on vectors, geometric properties and algebraic properties like addition, multiplication.
Check all NCERT solutions from class maths vector questions and solutions 12 to 12 at a single place, which maths vector questions and solutions 12 help in better understanding of concepts in a much easier way.
Latest : NEET exam preparation bothering you? Know More. Latest : Why settle for a classroom full of children when you can have your own personalized classroom? Question:1 Represent graphically a displacement of 40 km, east of north. Represent graphically a displacement of 40 km, east of north. N,S,E,W are maths vector questions and solutions 12 4 direction north,south,east,west respectively.
Question:2 1 Classify the following measures as scalars and vectors. Question:2 2 Classify the following measures as scalars and vectors. This is a vector quantity as it has both magnitude and direction.
Question:2 3 Classify the following measures as scalars and vectors. This is a scalar quantity as it has only magnitude. Question:2 4 Classify the following measures as scalars and vectors. Question:2 5 Classify the following measures as scalars and vectors. Question:2 6 Classify the following measures as scalars and vectors.
This is a Vector quantity as it has magnitude as well as direction. Question:3 Classify the following as scalar and vector quantities. Distance is a scalar quantity as it has only magnitude. Force is a vector quantity as it has both magnitude as well as direction.
Velocity is a vector quantity as it has both magnitude and direction. Question:4 In Fig Since vector and vector are starting from the same point, they are coinitial. Since Vector and Vector both have the same magnitude and same direction, they are equal.
Since vector and vector have the same magnitude but different direction, they are colinear and not equal. Question:5 Answer the following as true or false. True, and are collinear. False, because colinear means they are parallel to the same line but their magnitude can be maths vector questions and solutions 12 and hence this is a false statement. False, because any two non-colinear vectors can have the same magnitude.
False, because two colinear vectors with the same magnitude can have opposite direction. Question:1 Compute the magnitude of the following vectors:. Magnitude of.
Question:2 Write two different vectors having same magnitude. Two different Vectors having the same magnitude are. The magnitude of maths vector questions and solutions 12 vector. Question:3 Write two different vectors having same direction. Two different vectors having the same direction are:. Question:4 Find the values of x and y so that the vectors and are equal. Hence when. Question:5 Find the scalar and vector components of the vector with initial point 2, 1 and terminal point � 5, 7.
Hence scalar components are -7,6 and the vector maths vector questions and solutions 12. Question:6 Find the sum of the vectors.
Now, The sum of the vectors:. Question:7 Find the unit vector in the direction of the vector. A unit vector in the direction of. Question:8 Find the unit vector in the direction of vectorwhere P and Q are the points 1, 2, 3 and 4, 5, 6respectively. A vector in direction of PQ.
Magnitude of PQ. Now, unit vector in direction of PQ. Question:9 For given vectors, andfind the unit vector in the direction of the vector.
Now a unit vector in the direction of. Question Find a vector in the direction of vector which has magnitude 8 units. Given a vector. Question Show that the vectors and are collinear.
It can be seen. Hence. As we know. Whenever we havethe vector and will be colinear. Hence vectors and are collinear. Question Find the direction cosines of the vector. Hence direction cosine of are. Question Find the direction cosines of the vector joining the points A 1, 2, �3 and B �1, �2, 1directed from A to B. Hence Direction cosines of vector AB are. Hence direction cosines of this vectors is. Letand be maths vector questions and solutions 12 angle made by x-axis, y-axis and z- axis respectively.
Now as we know. Question 1 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are and respectively, in the ratio 2 : 1 internally. The position vector of the point R which divides the line segment PQ in Ch 1 Maths Class 10 Mcq Questions And Answers ratio m:n internally:.
And Hence. Question 2 Find the position vector of a point R which divides the maths vector questions and solutions 12 joining two points P and Q whose position vectors are and respectively, in the ratio 2 : 1 externally.
The position vector of the point R which divides the line segment PQ in ratio m:n externally:. Question Find the position vector of the mid point of the vector joining the points P 2, 3, 4 and Q 4, 1, �2. The position vector of R which divides PQ in half is given by:. Question Show that the points A, B and C with position vectors,respectively form the vertices of a right angled triangle. AS we can see. Hence ABC is a right angle triangle.
From triangles law of addition we have. From. Option C is False. Question If are two collinear vectors, then which of the following are incorrect: A for some saclar B C the respective components of are not proportional Maths vector questions and solutions 12 both the vectors have same direction, but different magnitudes.
If two vectors are collinear then, they have same direction or are parallel or anti-parallel. Therefore, They can be expressed in the form where a and b are vectors and is some scalar quantity.
Therefore, a is true. Now, b is a scalar quantity so its value may be equal to. Therefore, b is also true. C The vectors and are proportional, Therefore, c is not true. D The vectors and can have different magnitude as well as different directions. Therefore, d is not true. Therefore, the correct options are C and D. Question:1 Find the angle between two vectors with magnitudesrespectively having.
Hence the angle between the vectors is. Question:2 Find maths vector questions and solutions 12 angle between the vectors. Given two vectors. Now As we know. The angle between two vectors and is given by.
Hence the angle. Question:3 Find the projection of the vector on the vector. Projection of vector on.
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