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If [vecb" "vec(c)" "vecd]+[vec(c)" "vec(...

If `[vecb" "vec(c)" "vecd]+[vec(c)" "vec(a)" "vecd]+[vec(a)" "vecb" "vecd]=[a" "b" "c]` then show that the points with position vectors a,b,c and `vecd` are coplanar.

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Knowledge Check

  • If vec(a) xx vec(b)= vec(c ) xx vec(d), vec(a) xx vec(c )= vec(b) xx vec(d) , then

    A
    `(vec(a)-vec(d))//(vec(b)-vec(c ))`
    B
    `(vec(a)-vec(b))//(vec(c )-vec(d))`
    C
    `(vec(a)-vec(c ))//(vec(b)- vec(d))`
    D
    `(vec(a) + vec(b))//(vec(c ) + vec(d))`

  • Let vec(C ) = vec(A) + vec(B) ,

    A
    `|vec(C )|` is always greater than `|vec(A)|`
    B
    It is possible to have `|vec(C )| lt |vec(A)| and |vec(C )| lt |vec(B)|`
    C
    `|vec( C)|` is always equal to `|vec(A)| + |vec(B)|`
    D
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  • If vec(C ) = vec(A) - vec(B) , then:

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    B
    `bar(A) xx bar(C ) = bar(B) xx bar(C )`
    C
    `|vec(A) - vec(B)| gt |vec(B)| -|vec(B)|`
    D
    `vec(B) xx vec(A) = vec(C ) xx vec(A)`

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