Which among the statement/s below is/are true?i. The scalar product of two perpendicular vectors is sometimes zero.ii. The scalar product is maximum when the angle between the two vectors is 0.iii. When the angle between the two vectors is between 0 and 90, the cosine of the angle is greater thanzero and the scalar product is negative.iv. When the angle between the two vectors is between 90 and 180, the cosine of the angle is lesser thanzero and the scalar product is positive.Group of answer choicesiviiiiii
Question
Which among the statement/s below is/are true?i. The scalar product of two perpendicular vectors is sometimes zero.ii. The scalar product is maximum when the angle between the two vectors is 0.iii. When the angle between the two vectors is between 0 and 90, the cosine of the angle is greater thanzero and the scalar product is negative.iv. When the angle between the two vectors is between 90 and 180, the cosine of the angle is lesser thanzero and the scalar product is positive.Group of answer choicesiviiiiii
Solution
The correct statements are:
i. The scalar product of two perpendicular vectors is always zero. This is because the scalar product (or dot product) of two vectors is given by the product of their magnitudes and the cosine of the angle between them. For perpendicular vectors, this angle is 90 degrees, and the cosine of 90 degrees is zero.
ii. The scalar product is maximum when the angle between the two vectors is 0. This is because the cosine of 0 degrees is 1, which is the maximum value the cosine function can take. Therefore, the scalar product, being the product of the magnitudes of the vectors and the cosine of the angle between them, is maximum when the angle is 0.
iii. This statement is false. When the angle between the two vectors is between 0 and 90, the cosine of the angle is indeed greater than zero. However, since the scalar product is the product of the magnitudes of the vectors and the cosine of the angle between them, the scalar product is also greater than zero in this case.
iv. This statement is also false. When the angle between the two vectors is between 90 and 180, the cosine of the angle is indeed less than zero. However, since the scalar product is the product of the magnitudes of the vectors and the cosine of the angle between them, the scalar product is also less than zero in this case.
Similar Questions
What must be the dot product of two vectors that are perpendicular to each other or the angles between them is 90 degrees?Group of answer choicesnegativeminimumzeromaximum
If the dot product of two vectors A and B is negative, what does this indicate?Group of answer choicesThe vectors have opposite directionsThe vectors have zero magnitudeThe vectors are perpendicularThe vectors have the same direction
Which of the following will result in a scalar quantity?Group of answer choicesDot product of 2 vectorsEquilibrant of 2 vectorsResultant of 2 vectorsCross product of 2 vectors
Which of the following is NOT TRUE about negative vectors?Group of answer choicesThey are anti-parallel vectors.They have the same magnitude and opposite directions.They have the same magnitude with directions perpendicular with each other.They are not equal vectors.
If you have two vectors A and B, and A · B = 0, what can you conclude about the vectors?Group of answer choicesThey are perpendicular to each otherThey have the same magnitudeThey are parallel to each other.They have the same direction
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.