Vector $\vec{B}$ **has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of role="math" localid="1663647737200" $\vec{B}$ and (b) the angle that $\vec{B}$ makes with each coordinate axis.**

Question

Vector $\vec{B}$ **has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of role="math" localid="1663647737200" $\vec{B}$ and (b) the angle that $\vec{B}$ makes with each coordinate axis.**

Accepted Answer

(a) The magnitude of $\vec{B}$ is $| \vec{B} | = 7.81$

(b) The vector's angle with the x-axis is $α = 59.2 °$ , The vector's angle with the y-axis is $β = 39.8 °$ , The vector's angle with the z-axis is $γ = 67.4 °$

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Short Answer

Vector $\vec{B}$ **has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of role="math" localid="1663647737200" $\vec{B}$ and (b) the angle that $\vec{B}$ makes with each coordinate axis.**

Step by Step Solution

Step 1: Definition of magnitude and angle of vector

Step 2(a): Determine the magnitude

Step 3(b): Determine the angle that B→ makes with each coordinate axis

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Physics For Scientists & Engineers

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Short Answer

Vector B→ has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of role="math" localid="1663647737200" B→ and (b) the angle that B→ makes with each coordinate axis.

Step by Step Solution

Step 1: Definition of magnitude and angle of vector

Step 2(a): Determine the magnitude

Step 3(b): Determine the angle that B→ makes with each coordinate axis

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Vector $\vec{B}$ **has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of role="math" localid="1663647737200" $\vec{B}$ and (b) the angle that $\vec{B}$ makes with each coordinate axis.**