The vectors 𝑎⃗, 𝑏⃗⃗, 𝑐⃗ are as shown. a) Construct the vector 𝑎⃗ − 𝑏⃗⃗ + 𝑐⃗. b) If the vectors 𝑎⃗, 𝑏⃗⃗ are perpendicular and is |𝑎⃗|=4 and |𝑏⃗⃗|=3, determine|𝑎⃗+𝑏⃗⃗|

Question

The vectors 𝑎⃗, 𝑏⃗, 𝑐⃗ are as shown.

a) Construct the vector 𝑎⃗ − 𝑏⃗ + 𝑐⃗.

b) If the vectors 𝑎⃗, 𝑏⃗ are perpendicular and is |𝑎⃗|=4 and |𝑏⃗|=3, determine|𝑎⃗+𝑏⃗|

Answer 1

a) I'm rewriting this as (a^-> + c^->) - b^-> which is a very short vector pointing left plus a vector with length |b| but pointing downward, so the resultant is mostly down and a little to the left.

b) In component form, a^-> = <4,0> and b^-> = <0,3>, so a^-> + b^-> = <4,3>.