VECTOR ALGEBRA o. Let a i be a vector which makes an angle of 0 with a unit vector b. Then the unit vector ( a b) is [MP PET 99]. The perimeter of the triangle whose vertices have the position vectors ( i j k), (i k) and ( i 9k), is given by [MP PET 99] 7 7 7 7. The position vectors of two points A and B are i j k and i j k respectively. Then AB [BIT Ranchi 99]. The magnitudes of mutually perpendicular forces a, b and c are, 0 and respectively. Then the magnitude of its resultant is [IIT 98] 9 None. A unit vector a makes an angle with z-axis. If a i j is a unit vector, then a is equal to i j k i j k i j k [IIT 988] 6. If the position vectors of A and B are i 7k and i j k, then the direction cosine of AB along y-axis is [MNR 989] 6 6 7. If the resultant of two forces is of magnitude P and equal to one of them and perpendicular to it, then the other force is [MNR 986] P P P 8. The direction cosines of vector a i j k in the direction of positive axis of x, is [MP PET 99] 0 0 0 0 9. The point having position vectors i k, i j k, i j k are the vertices of [EAMCET 988] Right angled triangle Isosceles triangle Equilateral triangle Collinear 0. Let be distinct real numbers. The points with position vectors i j k, i j k, i j k [IIT Screening 99]
Are collinear Form an equilateral triangle Form a scalene triangle Form a right angled triangle. If a, b and a b, then a b [EAMCET 99] 6. If a and b are two non-zero and non-collinear vectors, then a + b and a b are [MP PET 997] Linearly dependent vectors Linearly independent vectors Linearly dependent and independent vectors. If the vectors 6i j k, i 6k and i 6j k form a triangle, then it is [Karnataka CET 999] Right angled Obtuse angled Equilteral Isosceles. If the resultant of two forces of magnitudes P and Q acting at a point at an angle of o 60 is 7Q, then P/Q is [Roorkee 999]. The direction cosines of the vector i j k are [Karnataka CET 000],, 6. The position vectors of A and B are i 9j k and 6i 8k respectively, then the magnitude of AB is [MP PET 000] 7. If the position vectors of P and Q are ( i j 7k) 8 60 6 6 and ( i j k), PQ is then [MP PET 00, 0] 8. If a is non zero vector of modulus a and m is a non-zero scalar, then ma is a unit vector if [MP PET 00] m m a a m m 9. The position vectors of the points A, B, C are ( i j k), ( i j k) and ( i j k) respectively. These points [Kurukshetra CEE 00] Form an isosceles triangle Form a right-angled triangle
Are collinear Form a scalene triangle 0. The vectors AB i k, and AC i j k are the sides of a triangle ABC. The length of the median through A is [AIEEE 00] 8 7 88. If the position vectors of the vertices A, B, C of a triangle ABC are 7j 0k, i 6j 6k and i 9j 6k respectively, the triangle is [UPSEAT 00] Equilateral Isosceles Scalene Right angled and isosceles also. The figure formed by the four points i j k, i, i k and k j is [MP PET 00] Rectangle Parallelogram Trapezium. ABC is an isosceles triangle right angled at A. Forces of magnitude, and 6 act along BC, CA and AB respectively. The magnitude of their resultant force is [Roorkee 999] 0. If ABCDEF is a regular hexagon and AB AC AD AE AF AD, then [RPET 98] 6. If ABCD is a parallelogram, AB i j k and AD i j k, then the unit vector in the direction of BD is [Roorkee 976] ( i j 8k) ( i j 8 k) ( i j 8k) ( i j 8 k) 6. If a, b and c be three non-zero vectors, no two of which are collinear. If the vector a b is collinear with c and b c is collinear with a, then ( being some non-zero scalar) a b 6c is equal to [AIEEE 00] a b c 0 7. If a i and b i j, then the unit vector along a b will be [RPET 98, 9] i j ( i j) i j i j 8. What should be added in vector a i j k to get its resultant a unit vector i [Roorkee 977]
i j k i j k i j k 9. If a i j k, b i j k and c i j, then the unit vector along its resultant is [Roorkee 980] i j k i k i k 0 0. In a regular hexagon ABCDEF, AE [MNR 98] AC AF AB AC AF AB AC AB AF. OD DA DB DC [IIT 988] OA OB OC OA OB BD OA OB OC. If a i j 8k and b i k, then the magnitude of a b [MP PET 996]. A, B, C, D, E are five coplanar points, then DA DB DC AE BE CE is equal to [RPET 999] DE DE DE ED. If a i j k, b i j k and c i j k, then a b c is [MP PET 00] i j i j i j i j. Five points given by A, B, C, D, E are in a plane. Three forces AC, AD and AE act at A and three forces AC AB DB BC CB, DB, EB act at B. Then their resultant is [AMU 00] 6. The sum of two forces is 8 N and resultant whose direction is at right angles to the smaller force is N. The magnitude of the two forces are [AIEEE 00],, 6,, 7 7. The unit vector parallel to the resultant vector of i j k and i j k is [MP PET 00] 7 (i 6j k) i j k 6 i j k ( i j 8k)
8. If a, b, c are the position vectors of the vertices A, B, C of the triangle ABC, then the centroid of ABC is [MP PET 987] a b c a b c b a c a b c 9. If in the given figure OA a, OB b and : PB m : n, A P B AP then OP [RPET 98; ] m a n b m n m a n b n a m b m n m a n b m n 0. If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that AC AB is [MNR 980; ] a b b a a b b a. The position vectors of A and B are i j k and i j k. The position vector of the middle point of the line AB is [MP PET 988] i j k i j k i j k. P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then OA OB OC OD [RPET 989; J & K 00] OP OP OP OP. If the position vectors of the points A, B, C, D be i k, i j k, i j k and i 0j 0k respectively, then [MNR 98] O AB CD AB CD AB CD. If C is the middle point of AB and P is any point outside AB, then [MNR 99; AIEEE 00] PA PB PC PA PB PC PA PB PC 0 PA PB PC 0. If position vectors of a point A is a + b and a divides AB in the ratio :, then the position vector of B is [MP PET 00] a b b a a b b