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In the Cartesian plane, O is the origin of the coordinate axes. A person starts at 0 and walks a distance of 3 units in the NORTH - EAST direction and reaches the point P. From P he walks 4 units distance parallel to NORTH-WEST direction and reaches the point Q. then the vector OQ in terms i and j. `(angleXOP=45^(0))` is

A

`bar(OQ)=(1)/(sqrt(2)) (-bari+7barj)`

B

`bar(OQ)=(1)/(sqrt(50)) (-bari+7barj)`

C

`bar(OQ)=(1)/(sqrt(10)) (-bari+7barj)`

D

`bar(OQ)=(1)/(sqrt(2))(bari-7barj)`

Text Solution

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A
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-PROPERTIES OF VECTORS
  1. Let p bari+3barj+4bark and sqrt(q)bari+5bark be two vectors where p, q...

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  2. Let f(t)=[t]bari+{t-[t]}barj+[t+1]bark where [.] denotes the greatest ...

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  3. If bara and barb two non collinear vectors then the points l(1)bara+m(...

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  4. If the vectors a bari+barj+bark, bari+b barj+bark, bari+barj+c bark (a...

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  5. The values of lambda such that (x, y, z) ne (0, 0, 0) and (i + j + 3k)...

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  6. A vector bare whose magnitude is 10 and d.c's are all equal angles mad...

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  7. ABC is any triangle and P is a point on the side BC. If Q is a point s...

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  8. In DeltaOAB, E is the mid point of AB and F is a point on OA such that...

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  9. ABC is a triangle and 'O', any point in the palne of the triangle. The...

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  10. In a parallelogram ABCD, P is the mid point of the side AD. The line ...

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  11. OABC is a tetrahedron D and E are the mid points of the edges bar(OA)...

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  12. In the Cartesian plane, O is the origin of the coordinate axes. A pers...

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  13. ABCDEF be a regular hexagon in the xy plane and bar(AB)=4bari. Then ba...

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  14. The projections of a vector on the three coordinate axes are 6, -3, 2 ...

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  15. If the vectors AB = -3i + 4k and AC = 5i - 2j + 4k are the sides of a ...

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  16. If bara and barb are non-collinear vectors, then the value of alpha fo...

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  17. A plane containing the point (3, 2, 0) and the line (x+1)/(1)=(y-2)/(5...

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