If a -2 k- b -2 -k- then c -2 -3 k- then the angle between 2 a - c and a - b is-A-B-C-D- 3 -4

The correct option is B π/32 a c=2( î+ĵ+2k̂) ( 2î+ĵ+3k̂)=ĵ+k̂ a+b=( î+ĵ+2k̂)+(2î ĵ k̂)=î+k̂ If θ is the angle between 2a c, a+b then cos θ =(0)(1)+(1)(0)+(1)(1 ...

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Byju's Answer

Standard IX

Mathematics

Angle between Two Vectors

If a =-î+ĵ+2 ...

Question

If $a = -^i +^j + 2^k$ , $b = 2^i -^j -^k$ then $c = - 2^i +^j + 3^k$ , then the angle between 2a-c and a+b is:

\frac{π}{4}

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\frac{π}{3}

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\frac{π}{2}

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\frac{3 π}{4}

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Solution

The correct option is B $\frac{π}{3}$
$2 a - c = 2 (-^i +^j + 2^k) - (- 2^i +^j + 3^k) =^j +^k$
$a + b = (-^i +^j + 2^k) + (2^i -^j -^k) =^i +^k$
If $θ$ is the angle between 2a-c, a+b then $c o s θ = \frac{(0) (1) + (1) (0) + (1) (1)}{\sqrt{1 + 1} \sqrt{1 + 1}} = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

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If a=−^i+^j+2^k, b=2^i−^j−^k then c=−2^i+^j+3^k, then the angle between 2a-c and a+b is:

The correct option is B π32a−c=2(−^i+^j+2^k)−(−2^i+^j+3^k)=^j+^k a+b=(−^i+^j+2^k)+(2^i−^j−^k)=^i+^k If θ is the angle between 2a-c, a+b then cosθ=(0)(1)+(1)(0)+(1)(1)√1+1√1+1=12⇒θ=π3

If $a = -^i +^j + 2^k$ , $b = 2^i -^j -^k$ then $c = - 2^i +^j + 3^k$ , then the angle between 2a-c and a+b is: