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MMLU-Pro / 9269 / What is the angle ϕ between …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

What is the angle ϕ\phi between a→=3.0i^−4.0j^\vec{a}=3.0 \hat{\mathrm{i}}-4.0 \hat{\mathrm{j}} and b→=\vec{b}= −2.0i^+3.0k^-2.0 \hat{\mathrm{i}}+3.0 \hat{\mathrm{k}} ? (Caution: Although many of the following steps can be bypassed with a vector-capable calculator, you will learn more about scalar products if, at least here, you use these steps.)
Plain-text mathematical notation (without MathML)
What is the angle ϕ between (a)→=3.0(i)^−4.0(j)^ and (b)→= −2.0(i)^+3.0(k)^ ? (Caution: Although many of the following steps can be bypassed with a vector-capable calculator, you will learn more about scalar products if, at least here, you use these steps.)
Original LaTeX notation
What is the angle $\phi$ between $\vec{a}=3.0 \hat{\mathrm{i}}-4.0 \hat{\mathrm{j}}$ and $\vec{b}=$ $-2.0 \hat{\mathrm{i}}+3.0 \hat{\mathrm{k}}$ ? (Caution: Although many of the following steps can be bypassed with a vector-capable calculator, you will learn more about scalar products if, at least here, you use these steps.)

category

physics

options

  1. 150 $^{\circ}$
  2. 45 $^{\circ}$
  3. 109 $^{\circ}$
  4. 180 $^{\circ}$
  5. 75 $^{\circ}$
  6. 60 $^{\circ}$
  7. 120 $^{\circ}$
  8. 135 $^{\circ}$
  9. 90 $^{\circ}$
  10. 105 $^{\circ}$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9269
task_id
4e6734b9-d09e-5a59-863e-5eb1cb026a51
task_key
default--test--9269
task_revision_id
1
config / split
default / test

Official source

initial import