Question

The angle between two vectors -2î + 3j + k.
and i + 2 - 4k is​

Answer 1

Answer:

Explanation:

VectorA= -2î ++3j +k

VectorB= î +2j-4k

Â. B= (-2î +3j+k) . î +2j-4k

-2+6-4

= 0

Â. B = |Â| |B| costhetha

0 =|A||B|costhetha

0/|A||B| = costhetha

0 =costhetha

Thetha = 90°

Answer 2

The angle between A and B is 90 degrees.

Explanation:

Vector A = -2i+3j+k

Vector B = i+2j-4k

Let $\theta$ is the angle between two vectors. It can be calculated using the concept of dot product as :

$A.B=|A||B|\ cos\theta$

$|A|=\sqrt{(-2)^2+3^2+1^2}=3.74$

$|B|=\sqrt{(1)^2+2^2+(-4)^2}=4.58$

$cos\theta=\dfrac{(-2i+3j+k){\cdot}(i+2j-4k)}{3.74\times 4.58}$

$cos\theta=0$

$\theta=90^{\circ}$

So, the angle between A and B is 90 degrees. Hence, this is the required solution.

Learn more :

Topic : Dot product

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