Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 40 of 50
What is the vector projection of \(\vec{E} = 2\hat{i} - 3\hat{j} + 6\hat{k}\) onto the direction of vector \(\vec{F} = \hat{i} + 2\hat{j} + 2\hat{k}\)?
A
1/2
B
8/3
C
3/5
D
5/7
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 8/3
Concept:
Finding the scalar projection of one vector onto another.

Formula:
$$\text{Projection} = \frac{\vec{E} \cdot \vec{F}}{|\vec{F}|}$$

Solution:
Step 1: Calculate the dot product \(\vec{E} \cdot \vec{F}\):
$$\vec{E} \cdot \vec{F} = (2)(1) + (-3)(2) + (6)(2) = 2 - 6 + 12 = 8$$
Step 2: Calculate the magnitude of the target vector \(\vec{F}\):
$$|\vec{F}| = \sqrt{1^2 + 2^2 + 2^2} = \sqrt{9} = 3$$
Step 3: Evaluate the projection:
$$\text{Projection} = \frac{8}{3}$$

Why other options are incorrect:
  • A, C, and D are incorrect fractions that result from arithmetic errors in the dot product or using the wrong vector's magnitude in the denominator.

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