Vectors in the Coordinate Plane: Component Form and Magnitude

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What is the component form of vector 𝑣 with an initial point 𝑃(0, −7) and a terminal point 𝑄(−9,0)?

(−9,7) (correct)

(−9, −7)

(9,7)

(0,0)

What is the result of 2𝐮 − 𝐯, expressed as a linear combination of vectors i and j, given 𝐮 = 〈−10,4〉 and 𝐯 = 〈2,3〉?

-12𝒊 + 𝒋

-2𝒊 - 5𝒋 (correct)

-14𝒊 + 𝒋

2𝒊 + 𝒋

What is the unit vector with the same direction as 𝐯 = 〈−4, −3〉?

< -4√2/7, -3√2/7 >

< -4/5, -3/5 > (correct)

< 4/5, 3/5 >

< -4/5, 3/5 >

What is the dot product of vectors 𝑢 =< 5,3 > and 𝑣 =< 12,4 >?

48 Signup and view all the answers

For two vectors to be orthogonal, the dot product must equal to __________________.

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What is the component form and magnitude of vector 𝑃𝑄?

<5, 2>, 5 Signup and view all the answers

What are the components of the vector 2𝑢 + 3𝑤?

<8, -7> Signup and view all the answers

Find a unit vector in the direction of the vector 𝑤 = 5𝑖 + 5𝑗.

<0.5𝑖 + 0.5𝑗> Signup and view all the answers

What is the magnitude and direction angle of the vector −3𝑖 − 5𝑗?

√34, -124.9° Signup and view all the answers

Given 𝐫 = 5𝐢 − 𝐣, what is the magnitude of 𝐫?

2√6 Signup and view all the answers

Vectors in the Coordinate Plane: Component Form and Magnitude

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Questions and Answers

What is the component form of vector 𝑣 with an initial point 𝑃(0, −7) and a terminal point 𝑄(−9,0)?

What is the result of 2𝐮 − 𝐯, expressed as a linear combination of vectors i and j, given 𝐮 = 〈−10,4〉 and 𝐯 = 〈2,3〉?

What is the unit vector with the same direction as 𝐯 = 〈−4, −3〉?

What is the dot product of vectors 𝑢 =< 5,3 > and 𝑣 =< 12,4 >?

For two vectors to be orthogonal, the dot product must equal to __________________.

What is the component form and magnitude of vector 𝑃𝑄?

What are the components of the vector 2𝑢 + 3𝑤?

Find a unit vector in the direction of the vector 𝑤 = 5𝑖 + 5𝑗.

What is the magnitude and direction angle of the vector −3𝑖 − 5𝑗?

Given 𝐫 = 5𝐢 − 𝐣, what is the magnitude of 𝐫?

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