If three vectors xa→−$$2b$$→$$+3c$$→ , −$$2a$$→$$+yb$$→−$$4c$$→ and −zb→$$+2c$$→ are coplanar, where a→ , b→ and c→ are unit (or$$ $$any) vectors, then:

Correct option is 4xy−2zx+3z−4=0

Questions

If three vectors $x \vec{a} - 2 \vec{b} + 3 \vec{c}$ , $- 2 \vec{a} + y \vec{b} - 4 \vec{c}$ and $- z \vec{b} + 2 \vec{c}$ are coplanar, where $\vec{a}$ , $\vec{b}$ and $\vec{c}$ are unit (or any) vectors, then:

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xy+3zx−3x=4

2xy−2zx−3z−4=0

4xy−3zx+3z=4

xy−2zx+3z−4=0

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detailed solution

Correct option is D

Conditions of coplanarity, coplanar vectors have scalar triple product as zero A→.(B→×C→)=0 or |x−23−2y−40−z2|=0 or x(2y−4z)+2(−4−0)+3(2z−0)=0 or 2xy−4zx−8+6z=0 or xy−2zx+3z−4=0

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If three vectors xa→−2b→+3c→ , −2a→+yb→−4c→ and −zb→+2c→ are coplanar, where a→ , b→ and c→ are unit (or any) vectors, then:

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If three vectors $x \vec{a} - 2 \vec{b} + 3 \vec{c}$ , $- 2 \vec{a} + y \vec{b} - 4 \vec{c}$ and $- z \vec{b} + 2 \vec{c}$ are coplanar, where $\vec{a}$ , $\vec{b}$ and $\vec{c}$ are unit (or any) vectors, then: