Section Formula for Internal and External Division in Vectors Class 12 OP Malhotra Exe-21B ISC Maths Solutions Ch-21. In this article you would learn about section formula for internal and external division with solved practice questions. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
Section Formula for Internal and External Division in Vectors Class 12 OP Malhotra Exe-21B ISC Maths Solutions Ch-21
| Board | ISC |
| Publications | S Chand |
| Subject | Maths |
| Class | 12th |
| Chapter-21 | Vectors |
| Writer | OP Malhotra |
| Exe-21(b) | Section Formula for Internal and External Division |
Section Formula for Internal and External Division in Vectors
Que-1: OA→ and OB→ are vectors a→ and b→ respectively and X and Y are points of trisection of A B. Find, in terms of a and b .
(i) OX→ and
(ii) OY→
Sol:
Que-2: OA→ and OB→ are vectors a→ and b→ respectively and P and Q are points 1/4 and 3/4 of the way along A B. Find, in terms of a→ and b→ .
(i) OP→ and (ii) OQ→.
Sol:
Que-3: A B C D is quadrilateral in which BC is parallel to AD and the ratio of the lengths BC: AD is 4:7. Taking AB→ and AD→ as representatives of vectors v→ and 7u→ respectively, find which vectors are represented by
(i) BC→
(ii) AC→
(iii) BD→
(iv) DC→
(v) AE→ where E is on BD such that BE = 4/11 BD in length;
(vi) AF→ where F is on AC such that AF = 7/11 AC.
Sol:
Que-4: In fig. given below, B E is median of triangle A B C and G divides B E in the ratio 2 : 1.
(i) If AB→ represents u→ and AC→ represents v→ , show that EB→ represents u→ – 1/2 v→ and AG→ represents 1/3(u→ + v→).
(ii) If CF is a median, and H divides C F in the ratio 2 : 1, show that AH→ represents 1/3(u→ + v→).
(iii) If AD is a median and K divides AD in the ratio 2 : 1, which vector does AK→ represents in terms of u→ and v→ ? What can you conclude about G, H, K ? What can you conclude about the medians of a triangle?
Sol:
Que-6: Four points A, B, C, D with position vectors a→ , b→ , c→ , d→ respectively are
such that 3a→ – b→ + 2c→ – 4d→ = 0→. Show that the four points are coplanar. Also, find the position vector of the points of intersection of lines AC and BD.
Sol:
This shows that the position vector of point P dividing AC in the ratio 2 : 3 is same as that of point dividing B D in the ratio 4 : 1. Hence A C and B D intersects at point P. Thus A, B, C and D are coplanar. Since P be the point of intersection of A C and B D.
Thus, P.V. of the point of intersection of lines AC and BD be ( 3a→ + 2c→ )/5 or ( b→ + 4d→ )/5.
–: End of Section Formula for Internal and External Division in Vectors Class 12 OP Malhotra Exe-21B ISC Maths Solutions :–
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