Orthogonality in Space Quest

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Perpendiculars in 3D

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Maryam Jarrah

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Orthogonality in Space Quest


Froggy Jumps Orthogonality in Space QuestVersión en línea Perpendiculars in 3D por Maryam Jarrah 1 Which condition shows two vectors are orthogonal in math terms? a v1 · v2 = 0 b v1 × v2 = 0 c \|v1\| = \|v2\| 2 In 3D, a line orthogonal to a plane is perpendicular to every line in that plane? a Yes b Only at the intersection point c No, only to one line 3 Are the x-axis and y-axis orthogonal in standard space? a Yes b Only in 2D c No 4 What is the relation of a line orthogonal to a plane? a It is perpendicular to all lines in the plane through their intersection b It lies on the plane c It is parallel to the plane 5 If two lines are parallel to the x- and y-axes respectively, are they orthogonal? a Only if they meet b No c Yes 6 Give an example of two orthogonal vectors in R3. a (1,1,0) and (1,0,0) b (1,0,0) and (0,1,0) c (1,0,0) and (1,0,1) 7 In a right triangle, sine is the ratio of which two parts? a Adjacent over Hypotenuse b Opposite over Hypotenuse c Hypotenuse over Opposite 8 For a right triangle with AB=4, AC=3, BC=5, sin angle ABC equals? a AC/BC = 3/5 b AC/AB = 3/4 c AB/BC = 4/5 9 Using the cosine law, c^2 = a^2 + b^2 − 2ab cos C. What is cos BÂC if AB=7, AC=6, BC=5? a 5/7 b -5/7 c 7/5 10 Which statement about a plane is true? a A plane is a flat two-dimensional surface with length and width b It has thickness c It is only a line 11 In a right isosceles triangle, the hypotenuse is what multiple of the equal legs? a The hypotenuse is twice the leg b The hypotenuse is the leg times √2 c The hypotenuse equals the leg 12 Three non-collinear points determine what geometric object? a One plane b One point c One line 13 Four vertices of any quadrilateral determine what? a Three planes b One line c One plane 14 A plane has no edges and extends how? a Has edges b Has finite size c Extends forever 15 Cosine law relation for side c opposite angle C is which form? a c^2 = a^2 + b^2 − 2ab cos C b c = a + b cos C c c^2 = a^2 + b^2 + 2ab cos C

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Orthogonality in Space Quest

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Orthogonality in Space QuestVersión en línea

por Maryam Jarrah

Which condition shows two vectors are orthogonal in math terms?

In 3D, a line orthogonal to a plane is perpendicular to every line in that plane?

Are the x-axis and y-axis orthogonal in standard space?

What is the relation of a line orthogonal to a plane?

If two lines are parallel to the x- and y-axes respectively, are they orthogonal?

Give an example of two orthogonal vectors in R3.

In a right triangle, sine is the ratio of which two parts?

For a right triangle with AB=4, AC=3, BC=5, sin angle ABC equals?

Using the cosine law, c^2 = a^2 + b^2 − 2ab cos C. What is cos BÂC if AB=7, AC=6, BC=5?

Which statement about a plane is true?

In a right isosceles triangle, the hypotenuse is what multiple of the equal legs?

Three non-collinear points determine what geometric object?

Four vertices of any quadrilateral determine what?

A plane has no edges and extends how?

Cosine law relation for side c opposite angle C is which form?