Question

Can you find at least one vector perpendicular to 3i-4j+7k​

Answer 1

Answer:

Concept used:

If two vectors are perpendicular to each other then their scalar product is zero

That is,

$\vec{a}\:$⊥$\:\vec{b}$ if and only if $\vec{a}.\vec{b}=0$

Let $\vec{a}=3\vec{i}-4\vec{j}+7\vec{k}$

we can find many vectors perpendicular to $\vec{a}$

For example,

$\vec{x}=7\vec{i}+7\vec{j}+\vec{k}$

$\vec{y}=10\vec{i}+25\vec{j}+10\vec{k}$

$\vec{a}.\vec{x}=21-28+7=0$

$\vec{a}.\vec{y}=30-100+70=0$

This implies,

$\vec{x}\:$⊥$\:\vec{a}$

$\vec{y}\:$⊥$\:\vec{a}$

Answer 2

Answer:

icap+ 2 j cap + 5/7 k cap

Explanation:

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