In the Cartesian plane, O is the origin of the coordinate axes. A person starts at O and walks a distance of 3 units in the NORTH-EAST direction and reaches the point P. From P he waks 4 units of distance parallel to NORTH-EAST direction and reaches the point Q. Express the vector OQ in terms of i and j (observe that ∠XOP = 45°).
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Answer:
OQ = -1√2 i + 7/√2 j
OQ = 5 units
Step-by-step explanation:
Correct Question is :
A person starts at O and walks a distance of 3 units in the NORTH-EAST direction and reaches the point P. From P he waks 4 units of distance parallel to NORTH-WEST direction and reaches the point Q
walks a distance of 3 units in the NORTH-EAST
=> OP = 3Cos45 i + 3Sin45j
=> OP = 3/√2 i + 3/√2 j
Now 4 units of distance parallel to NORTH-WEST
=> PQ = 4 Cos135 i + 4 Sin 135j
=> PQ = -4/√2 i + 4/√2 j
OQ = OP + PQ
=> OQ = 3/√2 i + 3/√2 j -4/√2 i + 4/√2 j
=> -1√2 i + 7/√2 j
OQ = -1√2 i + 7/√2 j
OQ = 5 units
as per Question :
OQ = OP + OQ = 7 units in NORTH-EAST
=> OQ = 7Cos45 i + 7 Sin45j = 7/√2 i + 7/√2 j
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