Question 1: Find the angle between two vectors and vector with magnitudes √3 and 2, respectively having
ANSWER:
Question 2: Find the angle between the vectors
ANSWER :  The given vectors are .
Question 3: Find the projection of the vector on the vector .
Question 4: Find the projection of the vector on the vector .
Question 5: Show that each of the given three vectors is a unit vector
Question 6: Find , if
ANSWER:
Question 7: Evaluate the product
ANSWER
Question 8: Find the magnitude of two vectors a and b, having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2.
Question 9: Find , if for a unit
ANSWER:
Question 10: Show that is perpendicular to ,for any two nonzero vectors a and b.
ANSWER : 
Question 11: If , then what can be concluded about the vector ?
Question 12:If are unit vectors such that , find the value of
ANSWER:
Question 13: If either vector a = 0, then b = 0. But the converse need not be true. Justify your answer with an example.
ANSWER : 
Question 14:
ANSWER :  The vertices of ΔABC are given as A (1, 2, 3), B (–1, 0, 0), and C (0, 1, 2).
Question 15: Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.
ANSWER :  The given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).
Question 16: Show that the vectors 2i  j k, i  3j  5k and 3i  4j  4k form the vertices of a right angled triangle.
Question 17: nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then is unit vector if
(A) λ = 1
(B) λ = –1
(c) a =  λ
(d) a = 1/ λ
ANSWER : Vector is a unit vector if
205 videos264 docs139 tests

1. What is vector algebra? 
2. How are vectors represented in vector algebra? 
3. What are the basic operations in vector algebra? 
4. How do you find the magnitude of a vector in vector algebra? 
5. What is the significance of vector algebra in reallife applications? 
205 videos264 docs139 tests


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