Linear algebra-3

Algebra Level 2

what is one vector orthogonal to $A=3\vec{i}+4\vec{j}-5\vec{k}$ where vectors $\vec{i},\vec{j},\vec{k}$ are unit vectors in the third dimension orthogonal to each other.

two vectors are said to be orthogonal if there is a right angle between them.

3\vec{i}+4\vec{j}+5\vec{k}

3\vec{i}+4\vec{j}-5\vec{k}

\vec{i}+\vec{j}+\vec{k}

2\vec{i}+3\vec{j}-5\vec{k}

1 solution

Aareyan Manzoor
May 20, 2017

the way to confirm if two vectors are orthogonal is to take the dot product and see if it is 0. dot product of two matrix $\vec{a}.\vec{b}=a_1b_1+a_2b_2+\cdots+a_n b_n$ where $a_i$ are the components of $\vec{a}$ and similarlty $b_i$ is the components of $\vec{b}$ . looking at the choices the only vector that satisfies is $(3\vec{i}+4\vec{j}-5\vec{k}).\boxed{(3\vec{i}+4\vec{j}+5\vec{k})}=3*3+4*4+(-5)*5=0$

Linear algebra-3

1 solution

0 pending reports