Find the distance of the point (2, 12, 5) from the point of inte

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

311.

Find the angle between the vector straight i with hat on top minus straight j with hat on top space and space straight j with hat on top space minus space straight k with hat on top.

960 Views

312.

Find the value of 'p' for which the vectors 3 straight i with hat on top plus 2 straight j with hat on top plus 9 straight k with hat on top space and space straight i with hat on top minus 2 straight p straight j with hat on top plus 3 straight k with hat on top are parallel.

184 Views

313.

If the cartesian equations of a line are fraction numerator 3 minus straight x over denominator 5 end fraction equals fraction numerator straight y plus 4 over denominator 7 end fraction equals fraction numerator 2 straight z minus 6 over denominator 4 end fraction comma write the vector equation for the line. 

140 Views

314. If space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space are space perpendicular space vectors comma space open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar space equals space 13 space and space open vertical bar straight a with rightwards arrow on top close vertical bar space equals 5 space and space find space the space value space of space open vertical bar straight b with rightwards arrow on top close vertical bar.
135 Views

Advertisement
315.

Show that the four points A, B, C and D with position vectors
4 straight i with hat on top plus 5 straight j with hat on top plus straight k with hat on top comma negative straight j with hat on top minus straight k with hat on top comma space 3 straight i with hat on top plus 9 straight j with hat on top plus 4 straight k with hat on top space and space 4 left parenthesis negative straight i with hat on top plus straight j with hat on top plus straight k with hat on top right parenthesis respectively are coplanar.

373 Views

316.

The scalar product of the vector straight a with rightwards arrow on top equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top with a unit vector along the sum of vectors straight b with rightwards arrow on top equals 2 straight i with hat on top plus 4 straight j with hat on top minus 5 straight k with hat on top space space and space straight c with rightwards arrow on top space equals space straight lambda straight i with hat on top plus 2 straight j with hat on top plus 3 straight k with hat on top is equal to one. Find the value of straight lambda and hence find the unit vector along straight b with rightwards arrow on top plus straight c with rightwards arrow on top.

336 Views

 Multiple Choice QuestionsLong Answer Type

Advertisement

317.

Find the distance of the point (2, 12, 5) from the point of intersection of the line 
straight r with rightwards arrow on top equals 2 straight i with hat on top minus 4 straight j with hat on top plus 2 straight k with hat on top plus straight lambda open parentheses 3 straight i with hat on top plus 4 straight j with hat on top plus 2 straight k with hat on top close parentheses space and space the space plane space straight r with rightwards arrow on top. open parentheses straight i with hat on top minus 2 straight j with hat on top plus straight k with hat on top close parentheses equals 0.


Any point in the line is
2 plus 3 straight lambda comma space minus 4 plus 4 straight lambda comma space space 2 plus 2 straight lambda
The vector equation of the plane is given as

straight r with rightwards arrow on top. space open parentheses straight i with hat on top minus 2 straight j close parentheses plus straight k right parenthesis space equals space 0
Thus space the space cartesian space equation space of space the space plane space is space straight x minus 2 straight y plus straight z equals space 0
Since space the space point space lies space in space the space plane
left parenthesis 2 plus 3 straight lambda right parenthesis 1 plus left parenthesis negative 4 plus 4 straight lambda right parenthesis thin space left parenthesis negative 2 right parenthesis plus left parenthesis 2 plus 2 straight lambda right parenthesis 1 space equals 0
rightwards double arrow space 2 plus 8 plus 2 plus 3 straight lambda minus 8 straight lambda plus 2 straight lambda equals 0
rightwards double arrow 12 minus 3 straight lambda equals 0
rightwards double arrow 12 equals space 3 straight lambda
rightwards double arrow straight lambda equals 4

Thus, the point of intersection of the line and the plane is:
2 plus 3 cross times 4 comma space minus 4 plus 4 cross times 4 comma space space 2 plus 2 cross times 4
rightwards double arrow 14 comma space 12 comma space 10
Distance between (2, 12, 5) and (14, 12, 10) is:
straight d equals square root of left parenthesis 14 minus 2 right parenthesis squared plus left parenthesis 12 minus 12 right parenthesis squared plus left parenthesis 10 minus 5 right parenthesis squared end root
rightwards double arrow straight d equals space square root of 144 plus 25 end root
rightwards double arrow space straight d equals square root of 169
rightwards double arrow straight d space equals space 13 space units

140 Views

Advertisement

 Multiple Choice QuestionsShort Answer Type

318.

If a unit vector straight a with rightwards arrow on top space equals space straight x straight i with hat on top plus 2 straight j with hat on top minus straight z straight k with hat on top and straight b with rightwards arrow on top space equals space 3 straight i with hat on top minus straight y straight j with hat on top plus straight k with hat on top are two equal vectors, then write the value of x+y+z.

161 Views

Advertisement
319.

If a unit vector straight a with rightwards arrow on top makes angle straight pi over 3 space with space straight i with hat on top comma space space space straight pi over 4 space with space straight j with hat on top space and space acute space angle space straight theta space with space straight k with hat on top comma space then find the value of straight theta.

151 Views

320.

If straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are two vectors such that open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar equals open vertical bar straight a with rightwards arrow on top close vertical bar comma then prove that vector 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top is perpendicular to vector straight b with rightwards arrow on top.

158 Views

Advertisement