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Ehsaan Memon
Asked: 2022-11-07T12:06:04+05:30 In:

Given two orthogonal vectors `vecA and vecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`vecP` is equal to
A. `vecA/2 + (vecAxxvecB)/2`
B. `vecA/2 + (vecBxxvecA)/2`
C. `(vecAxxvecB)/2 -vecA/2`
D. `vecA xxvecB`

Given two orthogonal vectors `vecA and vecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`vecP` is equal to
A. `vecA/2 + (vecAxxvecB)/2`
B. `vecA/2 + (vecBxxvecA)/2`
C. `(vecAxxvecB)/2 -vecA/2`
D. `vecA xxvecB`
Parabola
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  1. Correct Answer – b
    `vecPxxvecB=vecA-vecP and |vecA|=|vecB|=1 and vecA.vecB=0`is given
    Now `vecP xx vecB = vecA-vecP`
    `(vecPxxvecB) xxvecB= (vecA-vecP)xxvecB`
    (taking cross product with `vecB` on both sides)
    `or (vecP.vecB)vecB- (vecB.vec B)vecP=vecAxxvec B -vecP xx vecB`
    `or (vecP.vecB) vecB-vecP=vecA xx vecB-vecA+vecP`
    `or 2vecP = vecA-vecA-vecAxxvec B-(vecP.vecB)vecB`
    `or vecP= (vecA-vecAxxvecB=-(vecP.vecB)vecB)/2`
    taking dot product with `vecB` on both sides of (i) get
    `vecP.vecB=vecA.vecB-vecP.vecB`ltbr gt `Rightarrow vecP.vecB=0`
    `Rightarrow vecP=( vecA + vecBxxvecA)/2`
    Now
    `(vecP xx vecB) xx vecB= (vecP.vecB) vecB-(vecB.vecB) vecP=-vecP`
    `vecP,vecA,vecPxxvecB(=vecA-vecP)` are depenment
    Also `vecP.vecB=0`
    ` and |vecP|^(2)=|(vecA-vecAxxvecB)/2|^(2)`
    `(|vecA|^(2)+|vecAxxvecB|^(2))/4`
    `(1+1)/4=1/2or |vecP|=1/sqrt2`

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Aisha Chhabra
Asked: 2022-11-07T09:30:39+05:30 In:

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`vecP` is equal to
A. `vecA/2 + (vecAxxvecB)/2`
B. `vecA/2 + (vecBxxvecA)/2`
C. `(vecAxxvecB)/2 -vecA/2`
D. `vecA xxvecB`

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`vecP` is equal to
A. `vecA/2 + (vecAxxvecB)/2`
B. `vecA/2 + (vecBxxvecA)/2`
C. `(vecAxxvecB)/2 -vecA/2`
D. `vecA xxvecB`
Parabola
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  1. Correct Answer – b
    `vecPxxvecB=vecA-vecP and |vecA|=|vecB|=1 and vecA.vecB=0`is given
    Now `vecP xx vecB = vecA-vecP`
    `(vecPxxvecB) xxvecB= (vecA-vecP)xxvecB`
    (taking cross product with `vecB` on both sides)
    `or (vecP.vecB)vecB- (vecB.vec B)vecP=vecAxxvec B -vecP xx vecB`
    `or (vecP.vecB) vecB-vecP=vecA xx vecB-vecA+vecP`
    `or 2vecP = vecA-vecA-vecAxxvec B-(vecP.vecB)vecB`
    `or vecP= (vecA-vecAxxvecB=-(vecP.vecB)vecB)/2`
    taking dot product with `vecB` on both sides of (i) get
    `vecP.vecB=vecA.vecB-vecP.vecB`ltbr gt `Rightarrow vecP.vecB=0`
    `Rightarrow vecP=( vecA + vecBxxvecA)/2`
    Now
    `(vecP xx vecB) xx vecB= (vecP.vecB) vecB-(vecB.vecB) vecP=-vecP`
    `vecP,vecA,vecPxxvecB(=vecA-vecP)` are depenment
    Also `vecP.vecB=0`
    ` and |vecP|^(2)=|(vecA-vecAxxvecB)/2|^(2)`
    `(|vecA|^(2)+|vecAxxvecB|^(2))/4`
    `(1+1)/4=1/2or |vecP|=1/sqrt2`

    • 0
Sona Ehsaan Issac
Asked: 2022-11-06T16:15:03+05:30 In:

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
which of the following statements is false ?
A. vectors `vecP, vecA and vecP xx vecB` ar linearly dependent.
B. vectors `vecP, vecB and vecP xx vecB` ar linearly independent
C. `vecP` is orthogonal to `vecB` and has length `1/sqrt2`.
D. none of these

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
which of the following statements is false ?
A. vectors `vecP, vecA and vecP xx vecB` ar linearly dependent.
B. vectors `vecP, vecB and vecP xx vecB` ar linearly independent
C. `vecP` is orthogonal to `vecB` and has length `1/sqrt2`.
D. none of these
Parabola
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  1. Correct Answer – d
    `vecPxxvecB=vecA-vecP and |vecA|=|vecB|=1 and vecA.vecB=0`is given
    Now `vecP xx vecB = vecA-vecP`
    `(vecPxxvecB) xxvecB= (vecA-vecP)xxvecB`
    (taking cross product with `vecB` on both sides)
    `or (vecP.vecB)vecB- (vecB.vec B)vecP=vecAxxvec B -vecP xx vecB`
    `or (vecP.vecB) vecB-vecP=vecA xx vecB-vecA+vecP`
    `or 2vecP = vecA-vecA-vecAxxvec B-(vecP.vecB)vecB`
    `or vecP= (vecA-vecAxxvecB=-(vecP.vecB)vecB)/2`
    taking dot product with `vecB` on both sides of (i) get
    `vecP.vecB=vecA.vecB-vecP.vecB`ltbr gt `Rightarrow vecP.vecB=0`
    `Rightarrow vecP=( vecA + vecBxxvecA)/2`
    Now
    `(vecP xx vecB) xx vecB= (vecP.vecB) vecB-(vecB.vecB) vecP=-vecP`
    `vecP,vecA,vecPxxvecB(=vecA-vecP)` are depenment
    Also `vecP.vecB=0`
    ` and |vecP|^(2)=|(vecA-vecAxxvecB)/2|^(2)`
    `(|vecA|^(2)+|vecAxxvecB|^(2))/4`
    `(1+1)/4=1/2or |vecP|=1/sqrt2`

    • 0
Sahil Rao Subramanian
Asked: 2022-11-05T21:38:23+05:30 In:

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`(vecP xx vecB ) xx vecB` is equal to
A. `vecP`
B. `-vecP`
C. `2vecB`
D. `vecA`

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`(vecP xx vecB ) xx vecB` is equal to
A. `vecP`
B. `-vecP`
C. `2vecB`
D. `vecA`
Parabola
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  1. Correct Answer – b
    `vecPxxvecB=vecA-vecP and |vecA|=|vecB|=1 and vecA.vecB=0`is given
    Now `vecP xx vecB = vecA-vecP`
    `(vecPxxvecB) xxvecB= (vecA-vecP)xxvecB`
    (taking cross product with `vecB` on both sides)
    `or (vecP.vecB)vecB- (vecB.vec B)vecP=vecAxxvec B -vecP xx vecB`
    `or (vecP.vecB) vecB-vecP=vecA xx vecB-vecA+vecP`
    `or 2vecP = vecA-vecA-vecAxxvec B-(vecP.vecB)vecB`
    `or vecP= (vecA-vecAxxvecB=-(vecP.vecB)vecB)/2`
    taking dot product with `vecB` on both sides of (i) get
    `vecP.vecB=vecA.vecB-vecP.vecB`ltbr gt `Rightarrow vecP.vecB=0`
    `Rightarrow vecP=( vecA + vecBxxvecA)/2`
    Now
    `(vecP xx vecB) xx vecB= (vecP.vecB) vecB-(vecB.vecB) vecP=-vecP`
    `vecP,vecA,vecPxxvecB(=vecA-vecP)` are depenment
    Also `vecP.vecB=0`
    ` and |vecP|^(2)=|(vecA-vecAxxvecB)/2|^(2)`
    `(|vecA|^(2)+|vecAxxvecB|^(2))/4`
    `(1+1)/4=1/2or |vecP|=1/sqrt2`

    • 0
Alpa Chand Pandit
Asked: 2022-11-01T00:13:44+05:30 In:

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`(vecP xx vecB ) xx vecB` is equal to
A. `vecP`
B. `-vecP`
C. `2vecB`
D. `vecA`

Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then
`(vecP xx vecB ) xx vecB` is equal to
A. `vecP`
B. `-vecP`
C. `2vecB`
D. `vecA`
Parabola
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  1. Correct Answer – b
    `vecPxxvecB=vecA-vecP and |vecA|=|vecB|=1 and vecA.vecB=0`is given
    Now `vecP xx vecB = vecA-vecP`
    `(vecPxxvecB) xxvecB= (vecA-vecP)xxvecB`
    (taking cross product with `vecB` on both sides)
    `or (vecP.vecB)vecB- (vecB.vec B)vecP=vecAxxvec B -vecP xx vecB`
    `or (vecP.vecB) vecB-vecP=vecA xx vecB-vecA+vecP`
    `or 2vecP = vecA-vecA-vecAxxvec B-(vecP.vecB)vecB`
    `or vecP= (vecA-vecAxxvecB=-(vecP.vecB)vecB)/2`
    taking dot product with `vecB` on both sides of (i) get
    `vecP.vecB=vecA.vecB-vecP.vecB`ltbr gt `Rightarrow vecP.vecB=0`
    `Rightarrow vecP=( vecA + vecBxxvecA)/2`
    Now
    `(vecP xx vecB) xx vecB= (vecP.vecB) vecB-(vecB.vecB) vecP=-vecP`
    `vecP,vecA,vecPxxvecB(=vecA-vecP)` are depenment
    Also `vecP.vecB=0`
    ` and |vecP|^(2)=|(vecA-vecAxxvecB)/2|^(2)`
    `(|vecA|^(2)+|vecAxxvecB|^(2))/4`
    `(1+1)/4=1/2or |vecP|=1/sqrt2`

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