Question

Use the following vectors to answer each part. Give exact simplified answers. vec{u} = 7vec{i} + 5vec{j} - 9vec{k} and vec{w} = -3vec{i} + 5vec{j}. (a) 2vec{u} + 3vec{w} = (b) ||vec{u} + vec{w}|| = (c) (vec{u} cdot vec{w})vec{w} = (d) Find the vector component of vec{w} that is parallel to 7vec{j}. Express your answer as a vector. (e) Find a unit vector in the opposite direction of vec{u}.

          Use the following vectors to answer each part. Give exact simplified answers.
vec{u} = 7vec{i} + 5vec{j} - 9vec{k} and vec{w} = -3vec{i} + 5vec{j}.
(a) 2vec{u} + 3vec{w} =
(b) ||vec{u} + vec{w}|| =
(c) (vec{u} cdot vec{w})vec{w} =
(d) Find the vector component of vec{w} that is parallel to 7vec{j}. Express your answer as a vector.
(e) Find a unit vector in the opposite direction of vec{u}.

Use the following vectors to answer each part. Give exact simplified answers.
vecu = 7veci + 5vecj - 9veck and vecw = -3veci + 5vecj.
(a) 2vecu + 3vecw =
(b) ||vecu + vecw|| =
(c) (vecu cdot vecw)vecw =
(d) Find the vector component of vecw that is parallel to 7vecj. Express your answer as a vector.
(e) Find a unit vector in the opposite direction of vecu.

Added by Carol C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/03/2023

Step 1

First, let's find 3W: 3W = 3(-3i + 5j - k) = -9i + 15j - 3k Now, let's add U and 3W: Zu + 3w = (7i + 5j - 9k) + (-9i + 15j - 3k) = (7 - 9)i + (5 + 15)j + (-9 - 3)k = -2i + 20j - 12k So, the answer for (a) is $\boxed{-2i + 20j - 12k}$. (b) To find ||u + w||, Show more…

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Use the following vectors to answer each part. Give exact simplified answers. u = 7i + 5j - 9k and w = -3i + 5j. (a) 2u + 3w = (b) ||u + w|| = (c) (u · w)w = (d) Find the vector component of w that is parallel to 7j. Express your answer as a vector. (e) Find a unit vector in the opposite direction of u.