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Collinear Vectors

If an angle b...

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If an angle between vectors a and b is 120^° and |a|=3 and |b|=4 then length of vector (4a-3b) will be

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\to a

\to b

θ = \frac{2 π}{3}

between them. If

∣ ∣ \to a ∣ ∣ = 1

∣ ∣ ∣ \to b ∣ ∣ ∣ = 2,

{∣ ∣ ∣ (\to a + 3 \to b) \times (3 \to a - \to b) ∣ ∣ ∣}^{2}

\to a

\to b

be two vectors such that

| \to a | = 1,

| \to b | = 4

\to a \cdot \to b = 2.

\to c = (2 \to a \times \to b) - 3 \to b,

then the angle between

\to b

\to c

Q. If a, b, are three vectors such that each is inclined at an angle

π / 3

with the other two and

| a | = 1, | b | = 2, | c | = 3,

then the scalar product of the vectors

2 a + 3 b - 5 c

4 a - 6 b + 10 c

\to a

\to b

be two vectors such that

∣ ∣ ∣ 2 \to a + 3 \to b ∣ ∣ ∣ = ∣ ∣ ∣ 3 \to a + \to b ∣ ∣ ∣

and the angle between

\to a

\to b

60^{\circ} .

\frac{1}{8} \to a

is a unit vector, then

∣ ∣ ∣ \to b ∣ ∣ ∣

\to a

\to b

are two vectors such that

| \to a | = 1, | \to b | = 4, | \to c |^{2} = 192

\to a . \to b = 2

\to c = (2 \to a \times \to b) - 3 \to b

, then the angle between

\to b

\to c

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Collinear Vectors

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