### EDUCATION UPDATES

# MTH 103 TMA Questions $ Answers

`Question: Given vector ui3j 6k v2i6j 12k and w3i9j 18k What is the relationship between u v and w`

Answer:Parallel vectors

Question: What is the vector product of a2ijk and b4i2j 3k

Answer: 5i10j

Question: Find the acute angle to the nearest degree angle between the vectors a3i4j and b5i12j

Answer:130

Question: Determine the scalar product of the vectors u2i3j 6k and v3i 6j 2k

Answer:0

Question: A car is driven eastward for a distance of 5km then northward for 3km Determine the total displacement of the car from its starting point to the nearest km

Answer:6 km

Question: Find a vector that is of magnitude 6 units and is collinear to the vector ij

Answer:3sqrt2i3sqrt2j

Question: Find the equation of a line passing through the point 1 1 and perpendicular to the liney3x 50

Answer:3y x 20

Question: A straight line whose gradient is 2 passes through a point of intersection of the lines 4x5y7 and 2x5y 10 Find its equation

Answer:y2x5

Question: Determine the equation of a circle of radius 4 with centre 2 2

Answer: x2y2 4x 4y 80

Question: Determine the coordinated of the centre and radius of a circle 2x22y24x4y 50

Answer: 1 1 and 32

Question: Find the acute angle to the nearest degree angle between the vectors a3i4j andb5i12j

Answer:A: 130

Question: If the point C2 1 be the centre of a circle that passes through the point A 22 find the equation of the circle

Answer:A: x2y2 4x2y0

Question: Find the area of a triangle with vertices 3 1 0 0 and 1 2

Answer:A: 5 square units

Question: P Q and R are points 1 6 3 6 and 5 2 respectively Determine the length of the line joining the mid points of PQ and QR

Answer:A: 4sqrt 5

Question: Find the equation of a straight line passing through the points 2 3 and 2 5

Answer:A: 2yx 80

Question: Find the values of x on the curve yx33x3 6x 10 where the gradient is 3

Answer:A: 3 or 1

Question: Find the equation of the tangent to the curve yx3 x2 at the point 1 0

Answer:A: yx 1

Question: Find the equation of the normal to the curve yx3 x2 at the point 1 1

Answer:A: yx1

Question: If r 2i 4j s 2i 6j t 3i j find 2r ts

Answer:A: 3i 3j

Question: If r 2i 4j s 2i 6j t 3i j find magnitude of the vector 2r ts

Answer:A: 3sqrt2

Question: Let Z1 6i 4j 4k Z2 i 6j k find magnitude of the vector Z1 Z2

Answer:A: 5sqrt6

Question: Find the unit vector in the direction of vector b 3i 4j 5k

Answer:A: frac3i4j 5ksqrt2

Question: Determine the direction cosines l m n of the vector 3i 2 j 6k

Answer:A: 29 29 19

Question: The scalar product of vectors a and b where theta is the angle between them is

Answer:A: ab sin theta

Question: Determine the scalar product of vectors 2i 3 j 5k and 4i j 6k

Answer:A: 29

Question: Given a circle with centre at the origin which passes through the point 2 1 Find its equation

Answer:A: x2 y2 5 0

Question: Find the equation of the line which is parallel to the line 2y 3x 3 and passes through the midpoint of 23 and 4 5

Answer:A: 2y 3x 11

Question: A line AB passes through the point P 3 2 with gradient 2 Determine the equation of the line CD through P perpendicular to AB

Answer:A: 2y x 7

Question: Find the centre and radius of each of the circle x2 y2 2x 6y 15

Answer:A: 1 3 5

Question: Determine the equation of a straight line passing through the point 1 0 and 2 3

Answer:A: 3x y 3

Question: Determine the gradient of a straight line passing through the point 1 6 and 3 3

Answer:A: 4 Sep

Question: In triangle ABC the points L M N are the midpoints of the sides AB BC and CA respectively Which these expressions is true

Answer:overline2ABoverline3BCoverlineAC2overlineLC

Question: is the component contributions of the basis to the unit vector

Answer:Direction Cosines

Question: ABCD is a square quadrilateral with T and U the mid points of SP and QR respectively Which expressions is true

Answer:PQRS 2TU

Question: When two vectors are at right angles to each other the dot product is

Answer:Zero

Question: in analytic geometry of vector are the cosines of angles between the vector and the three coordinate axes

Answer:Direction Cosines

Question: If a10 b13 and the angle between a and b is 595 degree what is the scalar product of a and b

Answer:6598

Question: If ii 1 then ij

Answer: 1

Question: if aa1ia2ja3k and bb1ib2jb3k find ab

Answer:a1b1a2b2a3b3

Question: Find lmn of the vector r 2i 4j 3k

Answer:2sqrt29 4sqrt29 3sqrt29

Question: is a vector as a way of determining the magnitude and direction in its coordinate of x and y axis

Answer:Component of a vector in terms of unit vector

Question: is defined as the ratio of the vertical distance the line rises or falls to the horizontal distance

Answer:Gradient of a line

Question: The Locus of points at a distance of 3 from the point 0 0 is given by the equation

Answer:x2y29

Question: In Cartesian Coordinates the coordinates are given by the position

Answer:of a point in a plane

Question: The coordinates of the midpoint of a line segment is

Answer:the average of the coordinates of the endpoints

Question: The coordinate of the centre and the radius of the circle y2x2 14x 8y560 will be

Answer:7 4 are the coordinates or centre of the circle while 3 is the radius

Question: if a3i4j5k and b2ij7k Find ab

Answer:45

Question: If a 2i 4j 3k and b i 5j 2k Find the vector product of a and b

Answer:23i 7j 6k

Question: What is the gradient of the straight line and the angle of inclination of the points A2 3 and B4 5

Answer:gradient1 angle 45 degree

Question: If A is 3 6 and B is 4 8 Find the coordinate of the midpoint of AB

Answer: 3frac127

Question: Let A B C be the points 2 3 3 2 and 1 4 The length of AB yields

Answer:square root of 26

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