Name__________________________________ Topic 4 Review (Vectors) 1. Consider the points A (1, 5, 4), B (3, 1, 2) and D (3, 2), with (AD) perpendicular to (AB). k, (a) Find (i) (ii) , giving your answer in of k. (b) Show that = 7 k The C is such that = (c) Find the position vector of C (d) Find cos 2. Let = 3i + 4 + and = + 2 3k. The vector + is perpendicular to v j k w i j v pw w. – Find the value of p. 3. The point O has coordinates (0, 0, 0), point A has coordinates (1, 3) and point B has coordinates (–3, 4, –2, 2). (a) (i) Show that = (ii) Find (b) The line has equation L1 Write down the coordinates of two points on L1. (c) The line passes through A and is parallel to. L2 (i) Find a vector equation for giving your answer in the form = + r a L2, tb. (ii) Point C (k, 5)is on Find the coordinates of C. L2. –k, (d) The line has equation and passes through the point C. L3 Find the value of at C. p 4. The line is represented by = and the line by = L1 r1 L2 r2 The lines and intersect at point T. Find the coordinates of T. L1 L2 5. The diagram below shows a cuboid (rectangular solid) OJKLMNPQ. The vertex O is (0, 0, 0), J is (6, 0, 0), K is (6, 0, 10), M is (0, 7, 0) and Q is (0, 7, 10).
Name__________________________________ Topic 4 Review (Vectors) 1. Consider the points A (1, 5, 4), B (3, 1, 2) and D (3, k, 2), with (AD) perpendicular to (AB). (a) Find (i) (ii) , giving your answer in of k. (b) Show that k = 7 The C is such that = (c) Find the position vector of C (d) Find cos 2. Let v = 3i + 4 j + k and w = i + 2 j – 3k. The vector v + pw is perpendicular to w. Find the value of p. 3. The point O has coordinates (0, 0, 0), point A has coordinates (1, –2, 3) and point B has coordinates (–3, 4, 2). (a) (i) Show that = (ii) Find (b) The line L1 has equation Write down the coordinates of two points on L1. (c) The line L2 passes through A and is parallel to. (i) Find a vector equation for L2, giving your answer in the form r = a + tb. (ii) Point C (k, –k, 5)is on L2. Find the coordinates of C. (d) The line L3 has equation and passes through the point C. Find the value of p at C. 4. The line L1 is represented by r1 = and the line L2 by r2 = The lines L1 and L2 intersect at point T. Find the coordinates of T. 5. The diagram below shows a cuboid (rectangular solid) OJKLMNPQ. The vertex O is (0, 0, 0), J is (6, 0, 0), K is (6, 0, 10), M is (0, 7, 0) and Q is (0, 7, 10).
topic_4_vectors_review.docx