Question

if p=2i+3j-4k and q=5i+2j+4k find the angle between two vectors

Answer 1

Here's the answer to this question

Answer 2

The angle between p and q is 90 degrees.

Explanation:

Vector, $p=2i+3j-4k$

Vector, $q=5i+2j+4k$

We need to find the angle between two vectors. It can be calculated using dot product formula.

Magnitude of $|p|=\sqrt{2^2+3^2+(-4)^2} =5.385$

Magnitude of $|q|=\sqrt{5^2+2^2+(4)^2} =6.70$

Dot product formula,

$p.q=|p||q|\ cos\theta$

$cos\theta=\dfrac{p.q}{|p||q|}$

$cos\theta=\dfrac{(2i+3j-4k).(5i+2j+4k)}{5.385\times 6.70}$

$cos\theta=\dfrac{10+6-16}{36.079}$

$cos\theta=0$

$\theta=90^{\circ}$

So, the angle between p and q is 90 degrees. Hence, this is the required solution.

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Dot product

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