VECTOR TEST ( PLUS 2 OR GCE A - LEVEl)

TOPIC TEST ( VECTORS) Std. 12 Time: 1h 30 min [Note:- All vectors are shown by bold letters] 1. Write the direction ratios of the vector a = 2i + 3j – 6k and hence calculate its direction cosines. 2.Find the unit vector in the direction of the sum of the vectors, a = 2i + 2j – 5k and b = 2i + j + 3k . 3. If a = i + 2j + 3k , b = -2j + 4k and c = i – 2j + k , find ( a + b).c 4. Find the value of if the vector a = 2i+j + k is perpendicular to vector b = i – 2j + 3k. 5. Prove that the points 2i – j + k , i – 3j – 5k and 3i – 4j - 4k are the vertices of a right –angled triangle. 6 Prove the inequality where a and b are two vectors. 7.Find the angle between the vectors 3i - 2j - 6k and 4i – j + 8k 8. Find the vector product of the vectors a and b where a = 2i + 3j + 6k and b = 3i – 6j + 2k 9. Find a unit vector perpendicular to both of the vectors a = 4i – j + 3k and b = -2i + j – 2k. 10. Find the area of triangle PQR when P , Q , R have respective coordinates ( 1 , 3 , 2) , (2 , -1 , 1) and ( -1 , 2 ,3) 11. Prove that 12. Find a . b if 13. If a = i + 2j + 3k , b = -i + 2j + k and c = 3i + j , find such that a + b is perpendicular to c 14 Find the scalar projection of the vector a = i – 2j + k on the vector b = 4i – 4j + 7k. 15 If a = i + 2j – 3k and b = 3i – j + 2k, calculate the angle between the vectors 2a + b and a + 2b 16. Show that the vector i + j +k is equally inclined with coordinate axes. 17. For any vectors show that ( a + b).(a – b) = 18. Dot product of a vector with the vectors, I – j + k , 2i + j – 3k and i + j + k are respectively 4 , 0 and 2. Find the vector 19. Given vector a = i + 2j + 3k and b = 2i + 3j – 5k .Verify that a and (a X b ) are perpendicular to each other. 20. Find the magnitude of the vector a where a = (4j + 3k) X (i + j – k) 21. Find the sine of the angle between the vectors I + 3j + 2k and 2i – 4j + k 22 Let the position vectors of points P and Q be (3a – 2b) and ( a + b) respectively. Let another point M divides the line joining the points P and Q in the ratio, 3 : 2. Find the coordinates of M . ONLINE MATHS REVISION TESTS * * For CBSE (std 9 , 10 , 12) and Kerala (+2) ** Tests hit your e-mail inbox every week ** With answers/hints to work out. ** Currently in progress at affordable fee ** Provision for both online and face-face explanations 04812790195 e-mail : gntsgeorge@yahoo.co.in