Question

Angle between the two vectors vector a 3 icap + 4 j cap + 5 k cap and b 3 icap + 4 j cap and -5 will be

Answer 1

Answer:

the angle between them will be

90°

Answer 2

Angle between the two vectors vector a and b is 90°

Step-by-step explanation:

Let the given vectors are

$a=3i+4j+5k$

$b=3i+4j-5k$

The dot product of u and v is given by

$a\cdot b=(3i+4j+5k)\cdot(3i+4j-5k)\\\\a\cdot b=9+16-25\\\\a\cdot b=0$

The modulus of a and b is

$|a|=\sqrt{3^2+4^2+5^2}\\\\|a|=\sqrt{50}\\\\|a|=5\sqrt{2}$

$|b|=\sqrt{3^2+4^2+(-5)^2}\\\\|b|=\sqrt{50}\\\\|b|=5\sqrt{2}$

The angle between two vectors is given by

$\cos\theta=\frac{a\cdot b}{|a||b|}\\\\\cos\theta=\frac{0}{5\sqrt{2}\cdot5\sqrt{2}}\\\\\cos\theta=0\\\\\theta=90^{\circ}$

#Learn More:

Vector A +vector B =vector R

vector A2 +vector B2 =vector R2

find the angle between the two vectors

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