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Angle between Two Planes

For vectors A...

Question

For vectors $A, B$ and $C$ , given that $A + B = C$ and that $C$ is perpendicular to $A$ . Further, if $| A | = | C |$ , then what is the angle between $A$ and $B$ (in radians)?

\frac{π}{4}

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\frac{π}{2}

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\frac{3 π}{4}

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π

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Solution

The correct option is C $\frac{3 π}{4}$
Given that, $A + B = C$ and $C ⊥ A$ . It is shown in the diagram below.

From the diagram, we can say
$B cos θ = C$ and $B sin θ = A$
But, $A = C$ [also given]

$\Rightarrow B cos θ = B sin θ$
$\Rightarrow tan θ = 1$ or $θ = 45^{\circ}$
$∴$ Angle between A and B is $90^{\circ} + 45^{\circ} = 135^{\circ}$ or $\frac{3 π}{4} rad$

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Angle between Two Planes

Standard XII Mathematics

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For vectors A,B and C, given that A+B=C and that C is perpendicular to A. Further, if |A|=|C|, then what is the angle between A and B (in radians)?

The correct option is C 3π4 Given that, A+B=C and C⊥A. It is shown in the diagram below. From the diagram, we can say Bcosθ=C and Bsinθ=A But, A=C [also given] ⇒Bcosθ=Bsinθ ⇒tanθ=1 or θ=45∘ ∴ Angle between A and B is 90∘+45∘=135∘ or 3π4 rad

For vectors $A, B$ and $C$ , given that $A + B = C$ and that $C$ is perpendicular to $A$ . Further, if $| A | = | C |$ , then what is the angle between $A$ and $B$ (in radians)?