MA1S11 DISCRETE MATHEMATICS: TUTORIAL 3 1. Let v = h1;2iand w = h3; 1ibe two vectors in R2. (a) Draw arrows in the xy-plane which represent v and w and v+w.

MA1S11 DISCRETE MATHEMATICS: TUTORIAL 3

1. Let v = h1, 2i and w = h3, −1i be two vectors in R2 . (a) Draw arrows in the xy-plane which represent v and w and v+w. (b) Compute kvk and kwk and kv + wk. 2. Let u = h2, 6i and v = h5, 2i be two vectors in R2 . (a) Compute projv u (b) Draw arrows in the xy-plane which represent u and v and projv u. 3. Let u = h1, 2, 1i and v = h3, −1, 2i be two vectors in R3 . (a) Compute kuk and kvk and k2u − 3vk (b) Express u as the sum of a vector parallel to v and a vector orthogonal to v. 4. Let P (1, 2, −1) and Q(3, 4, 2) be two points in R3 . →

→

(a) Draw arrows in the xyz-space to represent the vectors OP , OQ →

and P Q. →

(b) Write the vector P Q in component form and compute the distance between P and Q.

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1. Let v = h1, 2i and w = h3, −1i be two vectors in R2 . (a) Draw arrows in the xy-plane which represent v and w and v+w. (b) Compute kvk and kwk and kv + wk. 2. Let u = h2, 6i and v = h5, 2i be two vectors in R2 . (a) Compute projv u (b) Draw arrows in the xy-plane which represent u and v and projv u. 3. Let u = h1, 2, 1i and v = h3, −1, 2i be two vectors in R3 . (a) Compute kuk and kvk and k2u − 3vk (b) Express u as the sum of a vector parallel to v and a vector orthogonal to v. 4. Let P (1, 2, −1) and Q(3, 4, 2) be two points in R3 . →

→

(a) Draw arrows in the xyz-space to represent the vectors OP , OQ →

and P Q. →

(b) Write the vector P Q in component form and compute the distance between P and Q.

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