Test Index

CBSE Class 12 Math 2018 Solved Paper

© examsnet.com
Question : 20
Total: 29
Let
→
a
 = 4
^
i
+5
^
j
−
^
k
 ,
→
b
 =
^
i
−4
^
j
+5
^
k
 and
→
c
 = 3
^
i
+
^
j
−
^
k
. Find a vector
→
d
 which is perpendicular to both
→
c
 and
→
b
 and
→
d
.
→
a
 = 21.
Solution:  
Let
→
d
 = x
^
i
+y
^
j
+z
^
k
since
→
d
 is perpendicular to
→
c
 and
→
b
 , so their dot product is zero
→
d
.
→
c
 = 0 and
→
d
.
→
b
 = 0
3x + y - z = 0 ... (1)
x - 4y + 5z = 0 ... (2)
Also given that
→
d
.
→
a
 = 21.
4x + 5y - z = 21 ... (3)
Solving all the equations simultaneously
x = −
1
3
 , y =
16
3
 , z =
13
3
→
d
 =
1
3
 (−
^
i
+16
^
j
+13
^
k
)
© examsnet.com
Go to Question:
Prev Question
Next Question