The i and j Plane (Leaving Cert Applied Maths): Quizzes

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The i and j Plane
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What is the i-j plane used to represent?

Vectors

What is the magnitude of unit vectors ii and jj?

Exactly 1 unit

Which axis does the ii-axis correspond to in direction?

Horizontal

What angle do unit vectors ii and jj make with each other?

90°

What does the vector 4i+3j4i + 3j represent?

4 units in ii-dir., 3 in jj-dir.

In the vector −5i+2j-5i + 2j, what does −5i-5i mean?

5 units in negative ii-direction

What is the formula for the magnitude of vector ai+bjai + bj?

a2+b2\sqrt{a^2 + b^2}

What is the magnitude of the vector 4i+3j4i + 3j?

5

Which formula finds the direction angle θ\theta of a vector?

tan⁡θ=j-comp.i-comp.\tan \theta = \frac{j\text{-comp.}}{i\text{-comp.}}

What is (2i−5j)+(5i+3j)(2i - 5j) + (5i + 3j)?

7i−2j7i - 2j

What is 3(2i−5j)−(5i+3j)3(2i - 5j) - (5i + 3j)?

i−18ji - 18j

When are two vectors perpendicular?

When product of slopes equals -1

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