If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ ABC, [ ∠ ABC is the angle between the vectors ].

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 10. Vector Algebra

Subject: Maths - Class 12^th

Q. No. 15 of Exercise 10.3

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15

If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC, [∠ABC is the angle between the vectors ].

Given points are A (1, 2, 3), B (-1, 0, 0) and C (0, 1, 2)

∠ABC is the angle between vectors

We know

⇒ ∠ABC = cos^-1(10/√102)

16

Chapter Exercises

Exercise 10.1

Exercise 10.2

Exercise 10.3

Exercise 10.4

Miscellaneous Exercise

1

Find the angle between two vectors with magnitudes √3 and 2 respectively having

2

Find the angle between the vectors

3

Find the projection of the vector on the vector

4

Find the projection of the vector on the vector

5

Show that each of the given three vectors is a unit vector :
Also, show that they are mutually perpendicular to each other.

6

Find if

7

Evaluate the product

8

Find the magnitude of two vectors , having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2.

9

Find if for a unit vector

10

If are such that is perpendicular to then find the value of λ.

11

Show that is perpendicular to for any two nonzero vectors .

12

If and then what can be concluded about the vector

13

If are unit vectors such that find the value of

14

If either vector then But the converse need not be true. Justify your answer with an example.

15

If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC, [∠ABC is the angle between the vectors ].

16

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.

17

Show that the vectors form the vertices of a right angled triangle.

18

If is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then is unit vector if