Question

Determine the angles which the vector a =5i+0j+5k makes with x,y and z axis

Answer 1

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Answer 2

Answer:

Angles made by x-axis is 45,  y-axis is 90° and z-axis is 45°

Step-by-step explanation:

Given the vector v=5i+0j+5k

We have to find the angles made by vector a with x,y and z axis.

Directions cosines are

$\alpha=cosa=\frac{v_{x}}{\sqrt{v_{x}^2+v_{y}^2+v_{z}^2}}=\frac{5}{\sqrt(5^{2}+0^{2}+5^{2})}=\frac{1}{\sqrt2}$

⇒ $\alpha=45^{\circ}$

$[tex]\beta =cosb=\frac{v_{y}}{\sqrt{v_{x}^2+v_{y}^2+v_{z}^2}}=\frac{0}{\sqrt(5^{2}+0^{2}+5^{2})}=0$

⇒ $\beta=90^{\circ}$

$\gamma=cosc=\frac{v_{z}}{\sqrt{v_{x}^2+v_{y}^2+v_{z}^2}}=\frac{5}{\sqrt(5^{2}+0^{2}+5^{2})}=\frac{1}{\sqrt2}$

⇒ $\gamma=45^{\circ}$

Hence, angles made by x-axis is 45,  y-axis is 90° and z-axis is 45°