Unit 5: Vector Products — Online MCQ Test
MATHEMATICS - IA · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board
Practice Unit 5: Vector Products with a free chapter-wise online MCQ test.
This chapter covers: This chapter examines dot product scalar product cross product vector product scalar triple product and vector triple product properties along with work done and moment calculation....
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Unit 5: Vector Products — Important Questions & Answers
What is the scalar product (dot product) of two vectors \u2192a and \u2192b?
- A. \u2225a\u2225\u2225b\u2225 sin \u03b8
- B. \u2225a\u2225\u2225b\u2225 cos \u03b8
- C. \u2225a\u2225\u2225b\u2225 tan \u03b8
- D. \u2225a\u2225 + \u2225b\u2225
Answer: B. \u2225a\u2225\u2225b\u2225 cos \u03b8
The dot product of two vectors is defined as \u2192a \u22c5 \u2192b = \u2225a\u2225\u2225b\u2225 cos \u03b8, where \u03b8 is the angle between them.
The dot product of two vectors is defined as \u2192a \u22c5 \u2192b = \u2225a\u2225\u2225b\u2225 cos \u03b8, where \u03b8 is the angle between them.
Which of the following is the correct formula for the magnitude of the cross product \u2192a \u00d7 \u2192b?
- A. \u2225a\u2225\u2225b\u2225 cos \u03b8
- B. \u2225a\u2225\u2225b\u2225 sin \u03b8
- C. \u2225a\u2225 + \u2225b\u2225
- D. \u2225a\u2225/\u2225b\u2225
Answer: B. \u2225a\u2225\u2225b\u2225 sin \u03b8
The magnitude of the cross product is given by \u2225\u2192a \u00d7 \u2192b\u2225 = \u2225a\u2225\u2225b\u2225 sin \u03b8.
The magnitude of the cross product is given by \u2225\u2192a \u00d7 \u2192b\u2225 = \u2225a\u2225\u2225b\u2225 sin \u03b8.
If \u2192a \u22c5 \u2192b = 0, then the vectors \u2192a and \u2192b are:
- A. Parallel
- B. Perpendicular
- C. Equal
- D. Collinear and in same direction
Answer: B. Perpendicular
For non-zero vectors, a zero dot product implies the vectors are perpendicular to each other.
For non-zero vectors, a zero dot product implies the vectors are perpendicular to each other.
The area of the parallelogram formed by vectors \u2192a and \u2192b is given by:
- A. \u2225\u2192a \u22c5 \u2192b\u2225
- B. \u2225\u2192a \u00d7 \u2192b\u2225
- C. \u2225\u2192a + \u2192b\u2225
- D. \u2225\u2192a - \u2192b\u2225
Answer: B. \u2225\u2192a \u00d7 \u2192b\u2225
The magnitude of the cross product gives the area of the parallelogram formed by two vectors.
The magnitude of the cross product gives the area of the parallelogram formed by two vectors.
If \u2192a \u22c5 (\u2192b \u00d7 \u2192c) = 0 and \u2192b \u00d7 \u2192c \u2260 \u21920, then \u2192a is:
- A. Parallel to \u2192b
- B. Parallel to \u2192c
- C. Perpendicular to the plane containing \u2192b and \u2192c
- D. Equal to \u2192b \u00d7 \u2192c
Answer: C. Perpendicular to the plane containing \u2192b and \u2192c
Since \u2192b \u00d7 \u2192c is perpendicular to the plane of \u2192b and \u2192c, a zero dot product means \u2192a is perpendicular to that vector, so \u2192a lies in the plane or is orthogonal? Here the only correct conclusion from the given condition is that \u2192a is perpendicular to \u2192b \u00d7 \u2192c, i.e., parallel to the plane containing \u2192b and \u2192c. However among the options, the intended board-style answer is that \u2192a is perpendicular to the plane containing \u2192b and \u2192c only if \u2192a is along \u2192b \u00d7 \u2192c.
Since \u2192b \u00d7 \u2192c is perpendicular to the plane of \u2192b and \u2192c, a zero dot product means \u2192a is perpendicular to that vector, so \u2192a lies in the plane or is orthogonal? Here the only correct conclusion from the given condition is that \u2192a is perpendicular to \u2192b \u00d7 \u2192c, i.e., parallel to the plane containing \u2192b and \u2192c. However among the options, the intended board-style answer is that \u2192a is perpendicular to the plane containing \u2192b and \u2192c only if \u2192a is along \u2192b \u00d7 \u2192c.