Vectors questions with solutions

Showing 1–10 of 116 questions

• A/RmediumMathematical tools and vectorVectors

  Choose the correct option for the given Assertion and Reason.

  Assertion

  The scalar triple product of three coplanar vectors is zero.

  Reason

  The absolute value of the scalar triple product equals the volume of the parallelepiped formed by the three vectors.

  Options

  • Option A

    Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

  • Option B

    Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.

  • Option C

    Assertion is true, but Reason is false.

  • Option D

    Assertion is false, but Reason is true.

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• MCQmediumMathematical tools and vectorVectors

  A vector makes equal acute angles with +x and +y and angle 60° with +z. Find its direction cosines.

  Options

  • Option A

    (√(3/8),√(3/8),1/2)

  • Option B

    (1/2,1/2,1/√2)

  • Option C

    (√3/2,√3/2,1/2)

  • Option D

    (1/√3,1/√3,1/√3)

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• MCQdifficultMathematical tools and vectorVectors

  If |A+B|=13, |A-B|=7 and |A|=|B|, find the magnitude of each vector.

  Options

  • Option A

    √(109/2)

  • Option B

    √109

  • Option C

    109/2

  • Option D

    √218

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• IntegermediumMathematical tools and vectorVectors

  For A⃗=î+ĵ+k̂, B⃗=2î-ĵ+k̂, C⃗=î+3ĵ-2k̂, evaluate A·(B×C).

  Your answer

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• MCQmediumMathematical tools and vectorVectors

  For A⃗=î+ĵ, B⃗=ĵ+k̂, C⃗=k̂+î, find A×(B×C).

  Options

  • Option A

    -î+ĵ

  • Option B

    î-ĵ

  • Option C

    -ĵ+k̂

  • Option D

    î-k̂

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• MCQmediumMathematical tools and vectorVectors

  A particle moves from A(1,2,-1) to B(5,-1,3). Find the direction cosine of its displacement with +z.

  Options

  • Option A

    4/√41

  • Option B

    -4/√41

  • Option C

    3/√41

  • Option D

    4/5

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• IntegermediumMathematical tools and vectorVectors

  For A⃗=î, B⃗=2ĵ, C⃗=3k̂, find A·(B×C).

  Your answer

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• Multi-correctmediumMathematical tools and vectorVectors

  Which dot-product identities are always correct?

  Select all that apply

  • Option A

    A·B=B·A

  • Option B

    A·(B+C)=A·B+A·C

  • Option C

    A·A=$\left\vert A\right\vert^2$

  • Option D

    A·B=|A||B| for all vectors

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• MCQmediumMathematical tools and vectorVectors

  Find a unit vector parallel to 2î+ĵ-2k̂ but directed oppositely.

  Options

  • Option A

    (-2î-ĵ+2k̂)/3

  • Option B

    (2î+ĵ-2k̂)/3

  • Option C

    (-2î+ĵ-2k̂)/3

  • Option D

    (-2î-ĵ+2k̂)/9

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →
• MCQmediumMathematical tools and vectorVectors

  Find the area of the triangle whose two sides from one vertex are 2î+ĵ and î+3ĵ.

  Options

  • Option A

    5/2

  • Option B

    5

  • Option C

    7/2

  • Option D

    7

  Check answerShow answer

  NEETJEE Mains

  Open question & full solution →