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Q 28.

Expert-verified
Found in: Page 801

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# Find $u+vandu-v$ also sketch $u,v,u+v,u-v$role="math" localid="1649603943715" $u=\left(3,6,11\right)andv=\left(1,-2,3\right)$

The required value of $u+v=\left(4,4,14\right)andu-v=\left(2,8,8\right)$.

See the step by step solution

## Step 1. Given information.

We have given vector $u=\left(3,6,11\right)andv=\left(1,-2,3\right)$

## Step 2. Find the values of u+v and u-v.

$u+v=\left({x}_{1}+{x}_{2},{y}_{1}+{y}_{2},{z}_{1}+{z}_{2}\right)\phantom{\rule{0ex}{0ex}}=\left(3+1,6+\left(-2\right),11+3\right)\phantom{\rule{0ex}{0ex}}=\left(4,4,14\right)\phantom{\rule{0ex}{0ex}}and\phantom{\rule{0ex}{0ex}}u-v=\left({x}_{1}-{x}_{2},{y}_{1}-{y}_{2},{z}_{1}-{z}_{2}\right)\phantom{\rule{0ex}{0ex}}=\left(3-1,6-\left(-2\right),11-3\right)\phantom{\rule{0ex}{0ex}}=\left(2,8,8\right)$

## Step 3. Sketch  u, v, u+v and u-v.

The graph of vector $u+v$.

The graph of vector $u-v$.