Class 11 Mathematics · Chapter 14 · Test 4
Scalar Triple Product
39 MCQs Covers the scalar triple product, volumes of the parallelepiped and tetrahedron, coplanarity conditions and the vector proofs (Ex 14.4).
39 questions · 30 min · 39 marks
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Sample questions
The first 5 of 39. Try each one, then tap to see the answer.
Question 1
The scalar triple product of u, v, w is
- Au × (v · w)
- Bu · (v × w)
- C(u · v) × w
- Du + (v × w)
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Answer: B
A dot product of one vector with the cross product of the other two.
Question 2
The scalar triple product is a
- Avector
- Bunit vector
- Cnull vector
- Dscalar
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Answer: D
It is a dot product, hence a number.
Question 3
u · (v × w) equals
- Av · (w × u) = w · (u × v)
- Bv · (u × w)
- C−w · (u × v)
- Du × (v · w)
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Answer: A
Cyclic permutation does not change the value.
Question 4
Interchanging two vectors in a scalar triple product
- Aleaves it unchanged
- Bdoubles it
- Cchanges its sign
- Dmakes it zero
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Answer: C
Rows of the determinant are swapped.
Question 5
The scalar triple product u · (v × w) is the volume of
- Aa tetrahedron with edges u, v, w
- Ba parallelepiped with edges u, v, w (in absolute value)
- Ca sphere
- Da triangle with sides u, v, w
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Answer: B
|u · (v × w)| = volume of the parallelepiped.
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