 Connect with us  `Question: Given vector ui3j 6k v2i6j 12k and  w3i9j 18k  What is the relationship between u v and  wAnswer:Parallel vectors      Question: What is the vector product of a2ijk and  b4i2j 3kAnswer:   5i10j  Question: Find the acute angle to the nearest degree angle between the vectors a3i4j and b5i12jAnswer:130Question: Determine the scalar product of the vectors u2i3j 6k and v3i 6j 2kAnswer:0Question: 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 kmAnswer:6 kmQuestion: Find a vector that is of magnitude 6 units and is collinear to the vector ijAnswer:3sqrt2i3sqrt2jQuestion: Find the equation of a line passing through the point 1 1 and perpendicular to the liney3x 50Answer: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 equationAnswer:y2x5Question:  Determine the equation of a circle of radius 4 with centre 2 2Answer: x2y2 4x 4y 80Question: Determine the coordinated of the centre and radius of a circle 2x22y24x4y 50Answer: 1  1 and  32      Question: Find the acute angle to the nearest degree angle between the vectors a3i4j andb5i12jAnswer:A: 130Question: If the point C2  1 be the centre of a circle that passes through the point A  22 find the equation of the circleAnswer:A: x2y2 4x2y0Question:  Find the area of a triangle with vertices 3 1 0 0 and 1 2Answer: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 QRAnswer:A: 4sqrt 5Question: Find the equation of a straight line passing through the points 2 3 and  2 5Answer:A: 2yx 80 Question: Find the values of x on the curve   yx33x3 6x 10  where the gradient is 3Answer:A:  3 or 1Question: Find the equation of the tangent to the curve   yx3 x2 at the point 1 0Answer:A: yx 1Question: Find the equation of the normal to the curve  yx3 x2   at the point 1 1Answer:A: yx1        Question: If r  2i  4j s  2i  6j t  3i  j find 2r tsAnswer:A: 3i  3j  Question: If r   2i  4j s  2i  6j t  3i  j find magnitude of the vector 2r tsAnswer:A: 3sqrt2Question: Let Z1  6i  4j 4k  Z2  i  6j  k find magnitude of the vector  Z1 Z2Answer:A: 5sqrt6Question: Find the unit vector in the direction of vector b  3i  4j  5kAnswer:A: frac3i4j 5ksqrt2Question: Determine the direction cosines l m n of the vector 3i  2 j 6kAnswer: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  6kAnswer:A: 29Question:  Given a circle with centre at the origin which passes through the point  2 1 Find its equationAnswer:A: x2  y2 5 0Question: 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 ABAnswer:A: 2y  x    7       Question: Find the centre and radius of each of the circle x2  y2 2x  6y  15Answer: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  3Answer:A: 4 SepQuestion: In triangle ABC the points L M N are the midpoints of the sides AB BC and CA respectively Which these expressions is trueAnswer:overline2ABoverline3BCoverlineAC2overlineLCQuestion:  is the component contributions of the basis to the unit vectorAnswer:Direction CosinesQuestion: ABCD is a square quadrilateral with T and U the mid points of SP and  QR respectively Which expressions is trueAnswer:PQRS 2TUQuestion: When two vectors are at right angles to each other the dot product is Answer:ZeroQuestion:  in analytic geometry of vector are the cosines of angles between the vector and the three coordinate axesAnswer:Direction CosinesQuestion: If a10 b13 and the angle between a and b is 595 degree what is the scalar product of a and bAnswer:6598Question: If ii  1 then ij  Answer: 1Question: if aa1ia2ja3k and bb1ib2jb3k find abAnswer:a1b1a2b2a3b3Question: Find lmn of the vector r  2i  4j  3kAnswer:2sqrt29 4sqrt29  3sqrt29Question:  is a vector as a way of determining the magnitude and direction in its coordinate of x and y axisAnswer:Component of a vector in terms of unit vectorQuestion:  is defined as the ratio of the vertical distance the line rises or falls to the horizontal distanceAnswer:Gradient of a lineQuestion: The Locus of points at a distance of 3 from the point 0 0 is given by the equationAnswer:x2y29Question: In Cartesian Coordinates the coordinates are given by the positionAnswer:of a point in a planeQuestion: The coordinates of the midpoint of a line segment isAnswer:the average of the coordinates of the endpointsQuestion: The coordinate of the centre and the radius of the circle y2x2 14x 8y560  will beAnswer:7 4 are the coordinates or centre of the circle while 3 is the radiusQuestion: if a3i4j5k  and b2ij7k Find abAnswer:45Question: If a  2i  4j  3k and b  i  5j  2k Find the vector product of a and bAnswer:23i  7j  6k Question: What is the gradient of the straight line and the angle of inclination of the points  A2  3 and B4 5Answer:gradient1 angle  45 degreeQuestion: If A is 3 6 and B is 4 8 Find the coordinate of the midpoint of ABAnswer: 3frac127Question: Let A B C be the points 2 3 3  2 and  1 4 The length of AB yieldsAnswer:square root of 26`