If a-1 and a-2 are two non collinear unit vectors inclided at 60- to each other then the value of a-1-a-2 -2 a1-a-2 isA- 1-2B- -1-2C- 2D- 1-4

The correct option is A |a_1| = |a_2| = 1 So (a_1 a_2) . (2a_1 and a_2) = 2 a_1^2 a_2^2 a_1 a_2 cos θ =1/2 ...

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Cross Product of Two Vectors

If a⃗1 and a⃗...

Question

If ${\to a}_{1}$ and ${\to a}_{2}$ are two non collinear unit vectors inclided at $60^{\circ}$ to each other then the value of ( ${\to a}_{1}$ - ${\to a}_{2}$ ) .( $\to 2 a_{1}$ + ${\to a}_{2}$ ) is

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{\to A}_{1}

{\to A}_{2}

| {\to A}_{1} | = 3, | {\to A}_{2} | = 5

| {\to A}_{1} + {\to A}_{2} | = 5

(2 {\to A}_{1} + 3 {\to A}_{2}) \cdot (2 {\to A}_{1} - 2 {\to A}_{2})

∣ ∣ {\to A}_{1} ∣ ∣ = 2, ∣ ∣ {\to A}_{2} ∣ ∣ = \to 3

∣ ∣ {\to A}_{1} + {\to A}_{2} ∣ ∣ = 3

({\to A}_{1} + 2 {\to A}_{2}) . (3 {\to A}_{1} - 4 {\to A}_{2})

The equation of the plane containing the lines

$\to r = {\to a}_{1} + λ {\to a}_{2} a n d \to r = {\to a}_{2} + μ {\to a}_{1}$ is

\to r = {\to r}_{1} + t {\to a}_{1}

\to r = {\to r}_{2} + t {\to a}_{2}

{\to r}_{1} = j, {\to a}_{1} = i + 2 j - k

{\to r}_{2} = i + j + k, {\to a}_{2} = - 2 i - 2 j

_{1}

_{2}

∣ ∣_{1} +_{2} ∣ ∣ = \sqrt{3}

(_{1} -_{2}) . (2_{1} +_{2})

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