General Physics - Vectors

We say that the displacement of a particle is a vector quantity. Our best justification for this assertion is

• displacement can be specified by a magnitude and a direction

• operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments

• a displacement is obviously not a scalar

• displacement can be specified by three numbers

• displacement is associated with motion, where velocity is a vector

Which of the following is an accurate statement?

• A vector cannot have zero magnitude if one of its components is not zero

• The magnitude of a vector can be less than the magnitude of one of its components.

• If the magnitude of vector A is less than the magnitude of vector B, then the x-component of A is less than the x-component of B.

• The magnitude of a vector can be positive or negative.

Which of the following diagram illustrates the relationship \(\vec c = \vec b - \vec a\)?

Vectors \(\vec A\) and \(\vec B\) lie in the \(xy\) plane. We can deduce that \(\vec A=\vec B\) if

• \({A^2}_x+{A^2}_y={B^2}_x+{B^2}_y\)

• \(A_x+A_y=B_x+B_y\)

• \(A_x=B_x\) and \(A_y=B_y\)

• \(\frac{A_y}{A_x}=\frac{B_x}{B_y}\)

• \(A_x=B_y\) and \(A_y=B_x\)

If the eastward component of vector \(\vec A\) is equal to the westward component of vector \(\vec B\) and their northward components are equal. Which one of the following statements about these two vectors is correct?

• Vector \(\vec A\) is parallel to vector \(\vec B\)

• Vectors \(\vec A\) and \(\vec B\) point in opposite directions.

• Vector \(\vec A\) is perpendicular to vector \(\vec B\)

• The magnitude of vector \(\vec A\) is equal to the magnitude of \(\vec B\).

• None of the statements.

Which of the following operations will not change a vector?

• Translate it parallel to itself.

• Rotate it

• Multiply it by a constant factor.

• Add a constant vector to it.

• Translate it perpendicular to itself.

• None of the choices.

If \(\vec A\) and \(\vec B\) are nonzero vectors for which \(\vec A \cdot \vec B=0\), it must follow that

• \(\vec A \times \vec B=0\)

• \(\vec A\) is parallel to \(\vec B\).

• \(|\vec A \times \vec B|=AB\)

• \(|\vec A \times \vec B|=1\)

• None of the statements.

What is the vector product of \(\vec A = 2.00 \hat i + 3.00 \hat j + 1.00 \hat k\) and \(\vec B = 1.00 \hat i - 3.00 \hat j - 2.00 \hat k\)?

• \(-3.00 \hat i + 5.00 \hat j - 9.00 \hat k\)

• \(-5.00 \hat i + 2.00 \hat j - 6.00 \hat k\)

• \(5\)

• \(2.00 \hat i -9.00 \hat j - 2.00 \hat k\)

• \(-9\)

What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

• 6.93

• -6.93

• 4.00

• -4.00

• 8.00

• 6.81

You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

• 63° N of E

• 50° N of E

• 57° N of E

• 69° N of E

If \(\vec A = 1.00 \hat i + 4.00 \hat j - 1.00 \hat k, \vec B = 3.00\hat i - 1.00 \hat j - 4.00 \hat k\) , and \(\vec C=-1.00\hat i + 1.00 \hat j\), then \(|(\vec A \times \vec B) \cdot \vec C|\)=?

• 18

• \(12.00 \hat i - 6.00 \hat j - 12\hat k\)

• \(-3.00\hat i -4.00 \hat j-4.00\hat k\)

• \(6.00 \hat i - 12.00 \hat j - 12\hat k\)

• \(12\sqrt{3}\)

• -7

• 7