Precalculus : Find the Product of a Vector and a Scalar

Study concepts, example questions & explanations for Precalculus

varsity tutors app store varsity tutors android store

Example Questions

Example Question #93 : Matrices And Vectors

Find the product of the vector  and scalar .

Possible Answers:

Correct answer:

Explanation:

When multiplying a vector by a scalar we multiply each component of the vector by the scalar and the result is a vector:

Example Question #2 : Find The Product Of A Vector And A Scalar

Find the vector given by the product: 

Possible Answers:

Correct answer:

Explanation:

Given a scalar k and a vector v, the vector given by their products is defined component-wise:

 .

Here, our product is:

Example Question #94 : Matrices And Vectors

This question refers to the previous question.

Simplify.

Possible Answers:

Correct answer:

Explanation:

In order to simplify this problem we need to multiply the scalar factor to each component of the vector.

In our case the scalar factor is 

Thus,

Example Question #95 : Matrices And Vectors

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

In order to determine the final value of the vector, distribute the scalar among each term in the vector.

Example Question #5 : Find The Product Of A Vector And A Scalar

If the vector from  to  was multiplied by a scale factor of 3, what is the new vector ?

Possible Answers:

Correct answer:

Explanation:

To find :

Subtract vector  from .

Multiply this vector by a scale of 3.

Example Question #6 : Find The Product Of A Vector And A Scalar

Find the product of: 

Possible Answers:

Correct answer:

Explanation:

When a scalar is multiplied to a vector, simply distribute that value for both terms in the vector.

Example Question #7 : Find The Product Of A Vector And A Scalar

When given a vector  and a scalar  what happens to the length and angle of  when multiplied with ?

Possible Answers:

 or the length of the product is the same as the original vector.

The angle is unchanged

 

 or the length of the product is  times as long as the original vector.

The angle is multiplied by .

 

 or the length of the product is  times the length of the original vector. 

The angle is unchanged.

 or the length of the product is the same as the original vector.

The angle is multiplied by .

 

 or the length of the product is  times the length of the original vector. 

The angle is multiplied by 

Correct answer:

 or the length of the product is  times the length of the original vector. 

The angle is unchanged.

Explanation:

In simple terms  is the hypotenuse of a triangle formed by the components of . So when you multiply  by  it mupltiplies all the componets by . This makes the length of the hypotensuse grow by  as demonstrated by  from the Pythagorean Theorem.

For the same reasons the angle does not change because the new longer triangle will be a similar triangle to the original triangle. 

Example Question #8 : Find The Product Of A Vector And A Scalar

Determine the product:  

Possible Answers:

Correct answer:

Explanation:

To find the product of the scalar and the vector, simply multiply the scalar throughout each term inside the vector.  Do not confuse this with the dot product or the norm of a vector.

The answer is:  

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: