**Question 1: **Find the vector projection of $\vec{A}$ on $\vec{B}$ where $\vec{A}$ = (2,0,6) and $\vec{B}$ = (3,1,2).

** Solution: **

According to the 3D calculator,

Step 1 : Given vectors are $\vec{A}$ = 2i + 0j + 6k and $\vec{B}$ = 3i + j + 2k

The magnitude of $\vec{B}$ is given by

|B| = $\sqrt{(3)^{2} + (1)^{2} + (2)^{2}}$
= $\sqrt{14}$
= 3.741.

Step 2 : Vector projection is given by

proj_{B}A = $\frac{\vec{A}.\vec{B}}{|\vec{B}|^{2}}$ $\vec{B}$

= $\frac{(2)(3)+(0)(1)+(6)(2)}{|\sqrt{14}|^{14}}$ (3, 1, 2)

= $\frac{6 + 12}{14}$ (3, 1, 2)

= 1.28 (3, 1, 2)

= (3.857 ,1.2857, 2.5714).

**Question 2: **Find the scalar projection of $\vec{A}$ on $\vec{B}$ where $\vec{A}$ = 3i + 4j and $\vec{B}$ = 2i - j

** Solution: **

According to the 2D Calculator,

Step 1 : Given vectors are $\vec{A}$ = 3i + 4j and $\vec{B}$ = 2i - j.

The magnitude of $\vec{B}$ is given by

|B| = $\sqrt{(2)^{2} + (1)^{2}}$
= $\sqrt{5}$
= 2.236

Step 2 : Scalar projection ia given by

proj_{B}A = $\frac{\vec{A}.\vec{B}}{|\vec{B}|}$

= $\frac{(3)(2) + (4)(-1)}{\sqrt{5}}$

= $\frac{2}{\sqrt{5}}$
= 0.8944.

The scalar projection of $\vec{A}$ on $\vec{B}$ is 0.8944.